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Will serve as a good reference text for researchers and advanced students in the fields of probability, stochastic processes, analysis, geometry, mathematical physics, and physics.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52138564649233,"sku":"NLS9781461266242","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781461266242.jpg?v=1757563618"},{"product_id":"stochastic-analysis-and-mathematical-physics-book-ab-cruzeiro-9780817642464","title":"Stochastic Analysis and Mathematical Physics","description":"An outgrowth of an ongoing workshop on stochastic analysis held in Lisbon. The nine survey articles in the volume extend concepts from classical probability and stochastic processes to a number of areas of mathematical physics. Will serve as a good reference text for researchers and advanced students in the fields of probability, stochastic processes, analysis, geometry, mathematical physics, and physics.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52139325587729,"sku":"NLS9780817642464","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9780817642464.jpg?v=1757568463"},{"product_id":"seminar-on-stochastic-processes-1985-book-cinlar-9781468467505","title":"Seminar on Stochastic Processes, 1985","description":"The 1985 Seminar on Stochastic Processes was held at the University of Florida, Gainesville, in March. It was the fifth seminar in a continuing series of meetings which provide opportunities for researchers to discuss current work in stochastic processes in an informal atmosphere. Previous seminars were held at Northwestern University, Evanston and the University of Florida, Gainesville. The participants' enthusiasm and interest have resulted in stimulating and successful seminars. We thank them for it, and we also thank those participants who have permitted us to publish their research here. The seminar was made possible through the generous supports of the Division of Sponsored Research and the Department of Mathematics of the university of Florida, and the Air Force Office of Scientific Research, Grant No. 82- 0189. We are grateful for their support. Finally, the comfort and hospitality we enjoyed in Gainesville were due to the splendid efforts of Professor Zoran Pop-Stojanovic. J. G.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52139376607505,"sku":"NLS9781468467505","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781468467505.jpg?v=1757568760"},{"product_id":"fractal-geometry-and-stochastics-ii-book-christoph-bandt-9783764362157","title":"Fractal Geometry and Stochastics II","description":"The second conference on Fractal Geometry and Stochastics was held at Greifs­ wald\/Koserow, Germany from August 28 to September 2, 1998. Four years had passed after the first conference with this theme and during this period the interest in the subject had rapidly increased. More than one hundred mathematicians from twenty-two countries attended the second conference and most of them presented their newest results. Since it is impossible to collect all these contributions in a book of moderate size we decided to ask the 13 main speakers to write an account of their subject of interest. The corresponding articles are gathered in this volume. Many of them combine a sketch of the historical development with a thorough discussion of the most recent results of the fields considered. We believe that these surveys are of benefit to the readers who want to be introduced to the subject as well as to the specialists. We also think that this book reflects the main directions of research in this thriving area of mathematics. We express our gratitude to the Deutsche Forschungsgemeinschaft whose financial support enabled us to organize the conference. The Editors Introduction Fractal geometry deals with geometric objects that show a high degree of irregu­ larity on all levels of magnitude and, therefore, cannot be investigated by methods of classical geometry but, nevertheless, are interesting models for phenomena in physics, chemistry, biology, astronomy and other sciences.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52139382702353,"sku":"NLS9783764362157","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783764362157.jpg?v=1757568802"},{"product_id":"probability-in-banach-spaces-6-book-haagerup-9781468467833","title":"Probability in Banach Spaces 6","description":"This volume contains a selection of papers by the participants of the 6. International Conference on Probability in Banach Spaces, Sand- bjerg, Denmark, June 16-D1, 1986. The conference was attended by 45 participants from several countries. One thing makes this conference completely different from the previous five ones, namely that it was ar- ranged jointly in Probability in Banach spaces and Banach space theory with almost equal representation of scientists in the two fields. Though these fields are closely related it seems that direct collaboration between researchers in the two groups has been seldom. It is our feeling that the conference, where the participants were together for five days taking part in lectures and intense discussions of mutual problems, has contributed to a better understanding and closer collaboration in the two fields. The papers in the present volume do not cover all the material pre- sented in the lectures; several results covered have been published else- where. The sponsors of the conference are: The Carlsberg Foundation, The Danish Natural Science Research Council, The Danish Department of Education, The Department of Mathematics, Odense University, The Department of Mathematics, Aarhus University, The Knudsen Foundation, Odense, Odense University, The Research Foundation of Aarhus University, The Thborg Foundation. The participants and the organizers would like to thank these institu- tions for their support. The Organizers. Contents A. de Acosta and M. Ledoux, On the identification of the limits in the law of the iterated logarithm in Banach spaces. . . . .","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52140164514065,"sku":"NLS9781468467833","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781468467833.jpg?v=1757572973"},{"product_id":"seminar-on-stochastic-processes-1982-book-cinlar-9780817631314","title":"Seminar on Stochastic Processes, 1982","description":"This volume consists of about half of the papers presented during a three-day seminar on stochastic processes held at Northwestern University in March 1982. This was the second of such yearly seminars aimed at bringing together a small group of researchers to discuss their current work in an informal atmosphere. The invited participants in this year's seminar were B. ATKINSON, R. BASS, K. BICHTELER, D. BURKHOLDER, K.L. CHUNG, J.L. DOOB, C. DOLEANS-DADE, H. FOLLMER, R.K. GETOOR, J. GLOVER, J. MITRO, D. MONRAD, E. PERKINS, J. PITMAN, Z. POP-STOJANOVIC, M.J. SHARPE, and J. WALSH. We thank them and the other participants for the lively atmosphere of the seminar. As mentioned above, the present volume is only a fragment of the work discussed at the seminar, the other work having been committed to other publications. The seminar was made possible through the enlightened support of the Air Force Office of Scientific Research, Grant No. 80-0252A. We are grateful to them as well as the publisher, Birkhauser, Boston, for their support and encouragement. E.C. , Evanston, 1983 Seminar on stochastic Processes, 1982 Birkhauser, Boston, 1983 GERM FIELDS AND A CONVERSE TO THE STRONG MARKOV PROPERTY by BRUCE W. ATKINSON 1. Introduction The purpose of this paper is to give an intrinsic characterization of optional (i.e., stopping) times for the general germ Markov process, which includes the general right process as a special case. We proceed from the general to the specific.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52140398739729,"sku":"NLS9780817631314","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9780817631314.jpg?v=1757574327"},{"product_id":"seminar-on-stochastic-processes-1984-book-cinlar-9781468467475","title":"Seminar on Stochastic Processes, 1984","description":"The1989SeminaronStochasticProcesseswasheldattheUniversityof CaliforniaatSanDiegoonMarch30,31andApril1, Hl89. Thiswastheninth inanannualseriesofmeetingswhichprovideresearcherswiththeopportunity todiscusscurrentworkonstochasticprocessesinaninformalandenjoyableat- mosphere. PreviousseminarswereheldatPrincetonUniversity, Northwestern University, theUniversityofFloridaandtheUniversityofVirginia. Theseminar hasgrownovertheyears, withatotalofseventy-fiveparticipantsin1989. Fol- lowingthesuccessfulformatofpreviousyears, therewerefiveinvitedlectures, deliveredby K. L. Chung, D. Dawson, R. Durrett, N. IkedaandT. Lyons, with theremainderoftimebeingdevotedtostructured, butlessformal, discussionson currentworkandproblems. Severalsmallergroupsalsoheldworkshopsessions onspecifictopicssuchas: mper-processes, diffusionsonfractalsandHarnack inequalities. Theparticipant. s'interestandenthusiasmcreatedalivelyandstim- ulatingcnvironmentfortheseminar. Asampleoftheresearchdiscussedthereis containedinthisvolume. Thc1989SeminarwasmadepossiblebythesupportoftheNationalScience Foundation, theNationalSecurityAgencyandtheUniversityofCaliforniaatSan Diego. Yeextendourthankstothem, andtothepublishcrBirkhauserBoston, fortheirsupportandencouragemcnt. Finally, thanksgotoLynn, yilliamsforher cheerfulassistancewiththeseminarorganizationandproductionofthisvolume. P. J. Fitzsimmons R. J. Williams LaJolla,1989 LISTOFPARTICIPANTS P. Arzberger M. Emery E. Perkins J. Pitman B. Atkinson S. N. Evans L. Pitt J. Azema N. Falkner M. Bachman P. Fitzsimmons A. O. Pittenger Z. Pop-Stojanovic M. Barlow R. K. Getoor R. Bass J. Glover S. Port C. Bezuidenhout H. Heyer P. Protter R. Blumenthal K. Hoffmann K. M. Rao G. Brosamler J. Horowitz J. Rosen C. Burdzy P. Hsu T. Salisbury D. Burkholder N. Ikeda M. J. Sharpe H. Cai O. Kallenberg C. T. Shih R. Carmona F. Knight A. Sznitman W. Chen-Masters Y. Kwon M. Taksar K. L. Chung T. Kurtz L. Taylor E. Cinlar T. Liggett S. J. Taylor M. Cranston T. Lyons G. Terdik R. Dalang P. March E. Toby R. DanteDeBlassie M. Marcus R. Tribe R. Darling P. McGill J. Walsh D. Dawson T. Mountford J. Watkins J. Deuschel B. Oksendal S. Weinryb N. Dinculeanu V. Papanicolaou R. Williams R. Durrett R. Pemantle Z. Zhao E. B. Dynkin M. Penrose W. Zheng TABLEOFCONTENTS R. F. BAS Aprobabilisticproofoftheboundary 1 and K. BURDZY Harnackprinciple J. -D. DEUSCHEL LogarithmicSobolevinequalitiesof 17 symmetricdiffusions S. N. EVANS RescalingthevacancyofaBoolean coverageprocess 23 TheBlumenthal-Getoor-McKean P. J. FITZSIMONS, R. K. GETOR Theoremrevisited 35 andM. J. SHARPE P. J. FITZSIMONS Localtimes, occupationtimes, andthe Lebesguemeasureoftherangeofa andS. C.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52140918636817,"sku":"NLS9781468467475","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781468467475.jpg?v=1757576099"},{"product_id":"barcelona-seminar-on-stochastic-analysis-book-nualart-9783034896771","title":"Barcelona Seminar on Stochastic Analysis","description":"During the of Fall 1991, The Centre de Recerca Matematica, a research institute sponsored by the Institut d'Estudis Catalans, devoted a quarter to the study of stochastic analysis. Prominent workers in this field visited the Center from all over the world for periods ranging from a few days to several weeks. To take advantage of the presence in Barcelona of so many special- ists in stochastic analysis, we organized a workshop on the subject in Sant Feliu de Guixols (Girona) that provided an opportunity for them to ex- change information and ideas about their current work. Topics discussed included: Analysis on the Wiener space, Anticipating Stochastic Calculus and its Applications, Correlation Inequalities, Stochastic Flows, Reflected Semimartingales, and others. This volume contains a refereed selection of contributions from some of the participants in this workshop. We are deeply indebted to the authors of the articles for these exposi- tions of their valuable research contributions. We also would like to thank all the referees for their helpful advice in making the volume a reflection of the dynamic interchange that characterized the workshop. The success of the Seminar was due essentially to the enthusiasm and stimulating discus- sions of all the participants in an informal and pleasant atmosphere. To all of them our warm gratitude.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52141580779793,"sku":"NLS9783034896771","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783034896771.jpg?v=1757577622"},{"product_id":"seminar-on-stochastic-processes-1989-book-e-cinlar-9781461280316","title":"Seminar on Stochastic Processes, 1989","description":"The1989SeminaronStochasticProcesseswasheldattheUniversityof CaliforniaatSanDiegoonMarch30,31andApril1, Hl89. Thiswastheninth inanannualseriesofmeetingswhichprovideresearcherswiththeopportunity todiscusscurrentworkonstochasticprocessesinaninformalandenjoyableat- mosphere. PreviousseminarswereheldatPrincetonUniversity, Northwestern University, theUniversityofFloridaandtheUniversityofVirginia. Theseminar hasgrownovertheyears, withatotalofseventy-fiveparticipantsin1989. Fol- lowingthesuccessfulformatofpreviousyears, therewerefiveinvitedlectures, deliveredby K. L. Chung, D. Dawson, R. Durrett, N. IkedaandT. Lyons, with theremainderoftimebeingdevotedtostructured, butlessformal, discussionson currentworkandproblems. Severalsmallergroupsalsoheldworkshopsessions onspecifictopicssuchas: mper-processes, diffusionsonfractalsandHarnack inequalities. Theparticipant. s'interestandenthusiasmcreatedalivelyandstim- ulatingcnvironmentfortheseminar. Asampleoftheresearchdiscussedthereis containedinthisvolume. Thc1989SeminarwasmadepossiblebythesupportoftheNationalScience Foundation, theNationalSecurityAgencyandtheUniversityofCaliforniaatSan Diego. Yeextendourthankstothem, andtothepublishcrBirkhauserBoston, fortheirsupportandencouragemcnt. Finally, thanksgotoLynn, yilliamsforher cheerfulassistancewiththeseminarorganizationandproductionofthisvolume. P. J. Fitzsimmons R. J. Williams LaJolla,1989 LISTOFPARTICIPANTS P. Arzberger M. Emery E. Perkins J. Pitman B. Atkinson S. N. Evans L. Pitt J. Azema N. Falkner M. Bachman P. Fitzsimmons A. O. Pittenger Z. Pop-Stojanovic M. Barlow R. K. Getoor R. Bass J. Glover S. Port C. Bezuidenhout H. Heyer P. Protter R. Blumenthal K. Hoffmann K. M. Rao G. Brosamler J. Horowitz J. Rosen C. Burdzy P. Hsu T. Salisbury D. Burkholder N. Ikeda M. J. Sharpe H. Cai O. Kallenberg C. T. Shih R. Carmona F. Knight A. Sznitman W. Chen-Masters Y. Kwon M. Taksar K. L. Chung T. Kurtz L. Taylor E. Cinlar T. Liggett S. J. Taylor M. Cranston T. Lyons G. Terdik R. Dalang P. March E. Toby R. DanteDeBlassie M. Marcus R. Tribe R. Darling P. McGill J. Walsh D. Dawson T. Mountford J. Watkins J. Deuschel B. Oksendal S. Weinryb N. Dinculeanu V. Papanicolaou R. Williams R. Durrett R. Pemantle Z. Zhao E. B. Dynkin M. Penrose W. Zheng TABLEOFCONTENTS R. F. BAS Aprobabilisticproofoftheboundary 1 and K. BURDZY Harnackprinciple J. -D. DEUSCHEL LogarithmicSobolevinequalitiesof 17 symmetricdiffusions S. N. EVANS RescalingthevacancyofaBoolean coverageprocess 23 TheBlumenthal-Getoor-McKean P. J. FITZSIMONS, R. K. GETOR Theoremrevisited 35 andM. J. SHARPE P. J. FITZSIMONS Localtimes, occupationtimes, andthe Lebesguemeasureoftherangeofa andS. C.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52141624819985,"sku":"NLS9781461280316","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781461280316.jpg?v=1757577772"},{"product_id":"stable-processes-and-related-topics-book-cambanis-9781468467802","title":"Stable Processes and Related Topics","description":"The Workshop on Stable Processes and Related Topics took place at Cor- nell University in January 9-13, 1990, under the sponsorship of the Mathemat- ical Sciences Institute. It attracted an international roster of probabilists from Brazil, Japan, Korea, Poland, Germany, Holland and France as well as the U. S. This volume contains a sample of the papers presented at the Workshop. All the papers have been refereed. Gaussian processes have been studied extensively over the last fifty years and form the bedrock of stochastic modeling. Their importance stems from the Central Limit Theorem. They share a number of special properties which facilitates their analysis and makes them particularly suitable to statistical inference. The many properties they share, however, is also the seed of their limitations. What happens in the real world away from the ideal Gaussian model? The non-Gaussian world may contain random processes that are close to the Gaussian. What are appropriate classes of nearly Gaussian models and how typical or robust is the Gaussian model amongst them? Moving further away from normality, what are appropriate non-Gaussian models that are sufficiently different to encompass distinct behavior, yet sufficiently simple to be amenable to efficient statistical inference? The very Central Limit Theorem which provides the fundamental justifi- cation for approximate normality, points to stable and other infinitely divisible models. Some of these may be close to and others very different from Gaussian models.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52141799407889,"sku":"NLS9781468467802","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781468467802.jpg?v=1757578285"},{"product_id":"stochastic-climate-models-book-peter-imkeller-9783034895040","title":"Stochastic Climate Models","description":"The proceedings of the summer 1999 Chorin workshop on stochastic climate models captures well the spirit of enthusiasm of the workshop participants engaged in research in this exciting field. It is amazing that nearly 25 years after the formal theory of natural climate variability generated by quasi-white-noise weather forcing was developed, and almost 35 years after J . M. Mitchell first suggested this mechanism as the origin of sea-surf ace-temperature fluctuations and climate variability, there have arisen so many fresh perspectives and new applications of the theory. The workshop has succeeded admirably in high- lighting these new aspects while clarifying the position of stochastic climate modelling within the general framework of climate research and mathematical modelling. The organizers can be congratulated in bringing together leading researchers covering a wide range of scientific expertise, from mathematicians concerned with the derivation of stochastic models from first principles, to app- lied climate modellers trying to understand the dynamics of the complex climate system. Following the first burst of stochastic modelling papers in the decade from the mid-seventies to the mid-eighties, in which the viability of the concept was demonstrated using relatively simple conceptual models, there was a lull of work in this field. One awaited the development of more sophisticated climate models with which one could carry out realistic quantitative analyses of the implications of stochastic forcing for the global climate system. Now that these models have become widely available, it is natural that one is witnessing a resurgence of stochastic modelling investigations.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52142255178001,"sku":"NLS9783034895040","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783034895040.jpg?v=1757579642"},{"product_id":"fractal-geometry-and-stochastics-ii-book-christoph-bandt-9783034895422","title":"Fractal Geometry and Stochastics II","description":"The second conference on Fractal Geometry and Stochastics was held at Greifs­ wald\/Koserow, Germany from August 28 to September 2, 1998. Four years had passed after the first conference with this theme and during this period the interest in the subject had rapidly increased. More than one hundred mathematicians from twenty-two countries attended the second conference and most of them presented their newest results. Since it is impossible to collect all these contributions in a book of moderate size we decided to ask the 13 main speakers to write an account of their subject of interest. The corresponding articles are gathered in this volume. Many of them combine a sketch of the historical development with a thorough discussion of the most recent results of the fields considered. We believe that these surveys are of benefit to the readers who want to be introduced to the subject as well as to the specialists. We also think that this book reflects the main directions of research in this thriving area of mathematics. We express our gratitude to the Deutsche Forschungsgemeinschaft whose financial support enabled us to organize the conference. The Editors Introduction Fractal geometry deals with geometric objects that show a high degree of irregu­ larity on all levels of magnitude and, therefore, cannot be investigated by methods of classical geometry but, nevertheless, are interesting models for phenomena in physics, chemistry, biology, astronomy and other sciences.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52142280048913,"sku":"NLS9783034895422","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783034895422.jpg?v=1757579694"},{"product_id":"seminar-on-stochastic-processes-1988-book-cinlar-9781461282174","title":"Seminar on Stochastic Processes, 1988","description":"The 1988 Seminar on Stochastic Processes was held at the University of Florida, Gainesville, March 3 through March 5, 1988. It was the eighth seminar in a continuing series of meetings which provide opportunities for researchers to discuss current work in stochastic processes in an informal and enjoyable atmosphere. Previous seminars were held at Princeton University, Northwestern University, the University of Florida and the University of Virginia. The participants' enthusiasm and interest have created stimulating and successful seminars. We thank those participants who have permitted us to publish their research in this volume. This year's invited participants included B. Atkinson, J. Azema, D. Bakry, P. Baxendale, J. Brooks, G. Brosamler, K. Burdzy, E. Cinlar, R. Darling, N. Dinculeanu, E. Dynkin, S. Evans, N. Falkner, P. Fitzsimmons, R. Getoor, J. Glover, V. Goodman, P. Hsu, J.-F. Le Gall, M. Liao, P. March, P. McGill, J. Mitro, T. Mountford, C. Mueller, A. Mukherjea, V. Papanicolaou, E. Perkins, M. Pinsky, L. Pitt, A. O. Pittenger, Z. Pop-Stojanovic, M. Rao, J. Rosen, T. Salisbury, C. Shih, M. 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This volume contains invited articles by leading probabilists highlighting these advances. Major areas covered include: percolation theory, random walks, interacting particle systems and topics related to statistical mechanics. Graduate students and researchers in probability theory and math physics will find this book a useful reference.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52144088023313,"sku":"NLS9781461265955","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781461265955.jpg?v=1757587352"},{"product_id":"diffusion-processes-and-related-problems-in-analysis-volume-i-book-pinsky-9781468405668","title":"Diffusion Processes and Related Problems in Analysis, Volume I","description":"During the weekend of March 16-18, 1990 the University of North Carolina at Charlotte hosted a conference on the subject of stochastic flows, as part of a Special Activity Month in the Department of Mathematics. This conference was supported jointly by a National Science Foundation grant and by the University of North Carolina at Charlotte. Originally conceived as a regional conference for researchers in the Southeastern United States, the conference eventually drew participation from both coasts of the U. S. and from abroad. This broad-based par- ticipation reflects a growing interest in the viewpoint of stochastic flows, particularly in probability theory and more generally in mathematics as a whole. While the theory of deterministic flows can be considered classical, the stochastic counterpart has only been developed in the past decade, through the efforts of Harris, Kunita, Elworthy, Baxendale and others. Much of this work was done in close connection with the theory of diffusion processes, where dynamical systems implicitly enter probability theory by means of stochastic differential equations. In this regard, the Charlotte conference served as a natural outgrowth of the Conference on Diffusion Processes, held at Northwestern University, Evanston Illinois in October 1989, the proceedings of which has now been published as Volume I of the current series. Due to this natural flow of ideas, and with the assistance and support of the Editorial Board, it was decided to organize the present two-volume effort.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52144406331665,"sku":"NLS9781468405668","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781468405668.jpg?v=1757588775"},{"product_id":"seminar-on-stochastic-analysis-random-fields-and-applications-iv-book-robert-dalang-9783764371319","title":"Seminar on Stochastic Analysis, Random Fields and Applications IV","description":"This volume contains the Proceedings of the Fourth Seminar on Stochastic Analy- sis, Random Fields and Applications, which took place at the Centro Stefano Fran- scini (Monte Verita) in Ascona (Ticino), Switzerland, from May 20 to 24, 2002. The first three editions of this conference occured in 1993, 1996 and 1999. The Seminar covered several topics: fundamental aspects of stochastic analysis, such as stochastic partial differential equations and random fields, and applications to current active fields such as probabilistic methods in fluid dynamics, biomathe- matics, and financial modeling. As in the previous editions, this last topic was the subject of the Fourth Minisymposium on Stochastic Methods in Financial Models. These proceedings aim to present key aspects of these topics to a larger audience. All papers in this volume have been refereed. A major topic within Stochastic Analysis is the area of random fields which includes as particular cases, Gaussian random fields, stochastic partial differential equations (s. p. d. e. 's) and stochastic differential equations with values in Banach spaces. In this framework, interesting new developments were presented in the theory of Gaussian random fields on manifolds with applications to astrophysics and neurosciences. Moreover, with the aim of modeling certain very irregular phe- nomena, a theory of s. p. d. e. 's driven by noises concentrated on hyperplanes was presented.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52333646381329,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52333646741777,"sku":"NLS9783764371319","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783764371319.jpg?v=1758155418"},{"product_id":"fractal-geometry-and-stochastics-vi-book-uta-freiberg-9783030596484","title":"Fractal Geometry and Stochastics VI","description":"This collection of contributions originates from the well-established conference series \"Fractal Geometry and Stochastics\" which brings together researchers from different fields using concepts and methods from fractal geometry.  Carefully selected papers from keynote and invited speakers are included, both discussing exciting new trends and results and giving a gentle introduction to some recent developments. The topics covered include Assouad dimensions and their connection to analysis, multifractal properties of functions and measures, renewal theorems in dynamics, dimensions and topology of random discrete structures, self-similar trees, p-hyperbolicity, phase transitions from continuous to discrete scale invariance, scaling limits of stochastic processes, stemi-stable distributions and fractional differential equations, and diffusion limited aggregation.   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This book documents the establishment of fractal geometry as a substantial mathematical theory. As in the previous volumes, which appeared in 1998 and 2000, leading experts known for clear exposition were selected as authors. They survey their field of expertise, emphasizing recent developments and open problems. Main topics include multifractal measures, dynamical systems, stochastic processes and random fractals, harmonic analysis on fractals.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52335201517841,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52335202140433,"sku":"NLS9783764370701","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783764370701.jpg?v=1758159292"},{"product_id":"stochastic-analysis-and-related-topics-book-a-stnel-9781461267317","title":"Stochastic Analysis and Related Topics","description":"This volume contains a large spectrum of work: super processes, Dirichlet forms, anticipative stochastic calculus, random fields and Wiener space analysis. The first part of the volume consists of two main lectures given at the third Silivri meeting in 1990: 1. Infinitely divisible random measures and superprocesses by D.A. Dawson, 2. Dirichlet forms on infinite dimensional spaces and appli- cations by M. Rockner. The second part consists of recent research papers all related to Stochastic Analysis, motivated by stochastic partial differ- ential equations, Markov fields, the Malliavin calculus and the Feynman path integrals. We would herewith like to thank the ENST for its material support for the above mentioned meeting as well as for the ini- tial preparation of this volume and to our friend and colleague Erhan Qmlar whose help and encouragement for the realization of this volume have been essential. H. Korezlioglu A. S. Ustiinel INFINITELY DIVISIBLE RANDOM MEASURES AND SUPERPROCESES DONALD A. DAWSON 1. Introduction.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52336876650769,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52336877273361,"sku":"NLS9781461267317","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781461267317.jpg?v=1758164825"},{"product_id":"diffusion-processes-and-related-problems-in-analysis-volume-ii-book-v-wihstutz-9781461267393","title":"Diffusion Processes and Related Problems in Analysis, Volume II","description":"During the weekend of March 16-18, 1990 the University of North Carolina at Charlotte hosted a conference on the subject of stochastic flows, as part of a Special Activity Month in the Department of Mathematics. This conference was supported jointly by a National Science Foundation grant and by the University of North Carolina at Charlotte. Originally conceived as a regional conference for researchers in the Southeastern United States, the conference eventually drew participation from both coasts of the U. S. and from abroad. This broad-based par- ticipation reflects a growing interest in the viewpoint of stochastic flows, particularly in probability theory and more generally in mathematics as a whole. While the theory of deterministic flows can be considered classical, the stochastic counterpart has only been developed in the past decade, through the efforts of Harris, Kunita, Elworthy, Baxendale and others. Much of this work was done in close connection with the theory of diffusion processes, where dynamical systems implicitly enter probability theory by means of stochastic differential equations. In this regard, the Charlotte conference served as a natural outgrowth of the Conference on Diffusion Processes, held at Northwestern University, Evanston Illinois in October 1989, the proceedings of which has now been published as Volume I of the current series. Due to this natural flow of ideas, and with the assistance and support of the Editorial Board, it was decided to organize the present two-volume effort.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52336948740369,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52336949395729,"sku":"NLS9781461267393","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781461267393.jpg?v=1758165042"},{"product_id":"stochastic-analysis-and-related-topics-vii-book-laurent-decreusefond-9781461266389","title":"Stochastic Analysis and Related Topics VII","description":"One of the most challenging subjects of stochastic analysis in relation to physics is the analysis of heat kernels on infinite dimensional manifolds. The simplest nontrivial case is that of thepath and loop space on a Lie group. In this volume an up-to-date survey of the topic is given by Leonard Gross, a prominent developer of the theory. Another concise but complete survey of Hausdorff measures on Wiener space and its applications to Malliavin Calculus is given by D. Feyel, one of the most active specialists in this area. Other survey articles deal with short-time asymptotics of diffusion pro- cesses with values in infinite dimensional manifolds and large deviations of diffusions with discontinuous drifts. A thorough survey is given of stochas- tic integration with respect to the fractional Brownian motion, as well as Stokes' formula for the Brownian sheet, and a new version of the log- Sobolev inequality on the Wiener space. Professional mathematicians looking for an overview of the state-of-the- art in the above subjects will find this book helpful. In addition, graduate students as well as researchers whose domain requires stochastic analysis will find the original results of interest for their own research. The organizers acknowledge gratefully the financial help ofthe University of Oslo, and the invaluable aid of Professor Bernt 0ksendal and l'Ecole Nationale Superieure des Telecommunications.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52337309679889,"sku":"NLS9781461266389","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781461266389.jpg?v=1758166232"},{"product_id":"random-walks-brownian-motion-and-interacting-particle-systems-book-h-kesten-9781461267706","title":"Random Walks, Brownian Motion, and Interacting Particle Systems","description":"This collection of articles is dedicated to Frank Spitzer on the occasion of his 65th birthday. The articles, written by a group of his friends, colleagues, former students and coauthors, are intended to demonstrate the major influence Frank has had on probability theory for the last 30 years and most likely will have for many years to come. Frank has always liked new phenomena, clean formulations and elegant proofs. He has created or opened up several research areas and it is not surprising that many people are still working out the consequences of his inventions. By way of introduction we have reprinted some of Frank's seminal articles so that the reader can easily see for himself the point of origin for much of the research presented here. These articles of Frank's deal with properties of Brownian motion, fluctuation theory and potential theory for random walks, and, of course, interacting particle systems. 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Mohammed, * Backward SDE's and Viscosity Solutions of Second Order Semilinear PDE's, by E. Pardoux. The main lectures are presented at the beginning of the volume. There is also a review paper at the third place about the stochastic calculus of variations on Lie groups. The contributing papers vary from SPDEs to Non-Kolmogorov type probabilistic models. We would like to thank * VISTA, a research cooperation between Norwegian Academy of Sciences and Letters and Den Norske Stats Oljeselskap (Statoil), * CNRS, Centre National de la Recherche Scientifique, * The Department of Mathematics of the University of Oslo, * The Ecole Nationale Superieure des Telecommunications, for their financial support. L. Decreusefond J. Gjerde B. 0ksendal A.S. Ustunel PARTICIPANTS TO THE 6TH WORKSHOP ON STOCHASTIC ANALYSIS Vestlia H yfjellshotell, Geilo, Norway, July 28 -August 4, 1996. E-mail: abc@gfm.cii.fc.ui.pt Aureli ALABERT Departament de Matematiques Laurent DECREUSEFOND Universitat Autonoma de Barcelona Ecole Nationale Superieure des Telecom- 08193-Bellaterra munications CATALONIA (Spain) Departement Reseaux E-mail: alabert@mat. uab.es 46, rue Barrault Halvard ARNTZEN 75634 Paris Cedex 13 Dept. of Mathematics FRANCE University of Oslo E-mail: decreuse@res.enst.fr Box 1053 Blindern Laurent DENIS N-0316 Oslo C.M.I.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52337519132945,"sku":"NLS9781461273851","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781461273851.jpg?v=1758166908"},{"product_id":"dynkin-festschrift-book-mark-i-freidlin-9781461266914","title":"The Dynkin Festschrift","description":"But Dynkin's most famous results in probability concern the theory of Markov processes. 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Many of the main ideas from probability in separable Banach spaces turned out to have one or more useful analogues for empirical processes. Tightness became asymptotic equicontinuity.  Metric entropy remained useful but also was adapted to metric entropy with bracketing, random entropies, and Kolchinskii-Pollard entropy. 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PreviousseminarswereheldatPrincetonUniversity, Northwestern University, theUniversityofFloridaandtheUniversityofVirginia. Theseminar hasgrownovertheyears, withatotalofseventy-fiveparticipantsin1989. Fol- lowingthesuccessfulformatofpreviousyears, therewerefiveinvitedlectures, deliveredby K. L. Chung, D. Dawson, R. Durrett, N. IkedaandT. Lyons, with theremainderoftimebeingdevotedtostructured, butlessformal, discussionson currentworkandproblems. Severalsmallergroupsalsoheldworkshopsessions onspecifictopicssuchas: mper-processes, diffusionsonfractalsandHarnack inequalities. Theparticipant. s'interestandenthusiasmcreatedalivelyandstim- ulatingcnvironmentfortheseminar. Asampleoftheresearchdiscussedthereis containedinthisvolume. Thc1989SeminarwasmadepossiblebythesupportoftheNationalScience Foundation, theNationalSecurityAgencyandtheUniversityofCaliforniaatSan Diego. Yeextendourthankstothem, andtothepublishcrBirkhauserBoston, fortheirsupportandencouragemcnt. Finally, thanksgotoLynn, yilliamsforher cheerfulassistancewiththeseminarorganizationandproductionofthisvolume. P. J. Fitzsimmons R. J. Williams LaJolla,1989 LISTOFPARTICIPANTS P. Arzberger M. Emery E. Perkins J. Pitman B. Atkinson S. N. Evans L. Pitt J. Azema N. Falkner M. Bachman P. Fitzsimmons A. O. Pittenger Z. Pop-Stojanovic M. Barlow R. K. Getoor R. Bass J. Glover S. Port C. Bezuidenhout H. Heyer P. Protter R. Blumenthal K. Hoffmann K. M. Rao G. Brosamler J. Horowitz J. Rosen C. Burdzy P. Hsu T. Salisbury D. Burkholder N. Ikeda M. J. Sharpe H. Cai O. Kallenberg C. T. Shih R. Carmona F. Knight A. Sznitman W. Chen-Masters Y. Kwon M. Taksar K. L. Chung T. Kurtz L. Taylor E. Cinlar T. Liggett S. J. Taylor M. Cranston T. Lyons G. Terdik R. Dalang P. March E. Toby R. DanteDeBlassie M. Marcus R. Tribe R. Darling P. McGill J. Walsh D. Dawson T. Mountford J. Watkins J. Deuschel B. Oksendal S. Weinryb N. Dinculeanu V. Papanicolaou R. Williams R. Durrett R. Pemantle Z. Zhao E. B. Dynkin M. Penrose W. Zheng TABLEOFCONTENTS R. F. BAS Aprobabilisticproofoftheboundary 1 and K. BURDZY Harnackprinciple J. -D. DEUSCHEL LogarithmicSobolevinequalitiesof 17 symmetricdiffusions S. N. EVANS RescalingthevacancyofaBoolean coverageprocess 23 TheBlumenthal-Getoor-McKean P. J. FITZSIMONS, R. K. GETOR Theoremrevisited 35 andM. J. SHARPE P. J. FITZSIMONS Localtimes, occupationtimes, andthe Lebesguemeasureoftherangeofa andS. C.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52338824282385,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52338824970513,"sku":"NLS9781461267140","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781461267140.jpg?v=1758169096"},{"product_id":"stochastic-modelling-in-physical-oceanography-book-robert-adler-9781461275336","title":"Stochastic Modelling in Physical Oceanography","description":"The study of the ocean is almost as old as the history of mankind itself. When the first seafarers set out in their primitive ships they had to understand, as best they could, tides and currents, eddies and vortices, for lack of understanding often led to loss of live. These primitive oceanographers were, of course, primarily statisticians. They collected what empirical data they could, and passed it down, ini- tially by word of mouth, to their descendants. Data collection continued throughout the millenia, and although data bases became larger, more re- liable, and better codified, it was not really until surprisingly recently that mankind began to try to understand the physics behind these data, and, shortly afterwards, to attempt to model it. The basic modelling tool of physical oceanography is, today, the partial differential equation. Somehow, we all 'know that if only we could find the right set of equations, with the right initial and boundary conditions, then we could solve the mysteries of ocean dynamics once and for all.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52340705526033,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52340709196049,"sku":"NLS9781461275336","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781461275336.jpg?v=1758171016"},{"product_id":"high-dimensional-probability-ii-book-david-mason-9781461271116","title":"High Dimensional Probability II","description":"High dimensional probability, in the sense that encompasses the topics rep- resented in this volume, began about thirty years ago with research in two related areas: limit theorems for sums of independent Banach space valued random vectors and general Gaussian processes. An important feature in these past research studies has been the fact that they highlighted the es- sential probabilistic nature of the problems considered. In part, this was because, by working on a general Banach space, one had to discard the extra, and often extraneous, structure imposed by random variables taking values in a Euclidean space, or by processes being indexed by sets in R or Rd. Doing this led to striking advances, particularly in Gaussian process theory. It also led to the creation or introduction of powerful new tools, such as randomization, decoupling, moment and exponential inequalities, chaining, isoperimetry and concentration of measure, which apply to areas well beyond those for which they were created. The general theory of em- pirical processes, with its vast applications in statistics, the study of local times of Markov processes, certain problems in harmonic analysis, and the general theory of stochastic processes are just several of the broad areas in which Gaussian process techniques and techniques from probability in Banach spaces have made a substantial impact. 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