{"title":"René L Schilling","description":null,"products":[{"product_id":"measures-integrals-and-martingales-book-ren-schilling-9781316620243","title":"Measures, Integrals and Martingales","description":"Measure and integration are key topics in many areas of mathematics, including analysis, probability, mathematical physics and finance. This book offers a concise yet elementary introduction in which the theory is quickly and simply developed. Few prerequisites are required, making the text suitable for undergraduate lecture courses or self-study.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ GARDNERS","offer_id":50520025792785,"sku":"NGR9781316620243","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51023002927377,"sku":"NIN9781316620243","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52666328875281,"sku":"NLS9781316620243","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ VERY_GOOD \/ SBYB","offer_id":53110769090833,"sku":"CIN1316620247VG","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/1316620247.jpg?v=1750921018"},{"product_id":"counterexamples-in-measure-and-integration-book-franziska-khn-9781316519134","title":"Counterexamples in Measure and Integration","description":"This is a perfect companion to any course on measure theory, integration, real and functional analysis, providing more than 300 examples and counterexamples to the otherwise often rather theoretical courses. By knowing 'what may go wrong' students will gain a better understanding of the standard course material.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51023442608401,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51023443132689,"sku":"NIN9781316519134","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/1316519139.jpg?v=1751239543"},{"product_id":"wahrscheinlichkeit-book-ren-schilling-9783110350654","title":"Wahrscheinlichkeit","description":"Die Wahrscheinlichkeitstheorie gehört zu den Kerndisziplinen der modernen Mathematikausbildung. Sie ist die Grundlage für alle Modelle, die „Risiko\" und „Unsicherheit\" einbeziehen. Dieses Lehrbuch gibt einen direkten, verlässlichen und modernen Zugang zu den wichtigsten Ergebnissen der mathematischen Wahrscheinlichkeitstheorie. Aufbauend auf dem Band „Maß \u0026amp; Integral\" werden zunächst elementare Fragen Wahrscheinlichkeitsverteilungen, Zufallsvariable, Unabhängigkeit, bedingte Wahrscheinlichkeiten und charakteristische Funktionen – bis hin zu einfachen Grenzwertsätzen behandelt. Diese Themen werden dann um das Studium von Summen unabhängiger Zufallsvariablen – Gesetze der Großen Zahlen, Null-Eins-Gesetze, random walks, zentraler Grenzwertsatz von Lindeberg-Feller – ergänzt. Allgemeine bedingte Erwartungen, Anwendungen von charakteristischen Funktionen und eine Einführung in die Theorie unendlich teilbarer Verteilungen und der großen Abweichungen runden die Darstellung ab. In gleicher Ausstattung erscheint der Folgeband „Martingale \u0026amp; Prozesse\".    Lösungen zu den im Buch befindlichen Übungsaufgaben unter: http:\/\/www.motapa.de\/stoch\/index.shtml","brand":"WoB","offers":[{"title":"US \/ NEW \/ INGRAM","offer_id":51061382873361,"sku":"NIN9783110350654","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52487947288849,"sku":"NLS9783110350654","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3110350653.jpg?v=1751064150"},{"product_id":"martingale-und-prozesse-book-ren-schilling-9783110350678","title":"Martingale und Prozesse","description":"This is the third volume of the series \"Moderne Stochastik\" (Modern Stochastics). As a follow-up to the volume \"Wahrscheinlichkeit\" (Probability Theory) it gives an intrdouction to dynamical aspects of probability theory using stochastic processes in discrete time. The first part of the book covers discrete martingales - their convergenc behaviour, optional sampling and stopping, uniform integrability and essential martingale inequalities. The power of martingale techniques is illustrated in the chapters on applications of martingales in classical probability and on the Burkholder-Davis-Gundy inequalities. The second half of the book treats random walks on Zd and Rd, their fluctuation behaviour, recurrence and transience. The last two chapters give a brief introduction to probabilistic potential theory and an outlook of further developments: Brownian motion and Donsker's invariance principle      Contents Fair Play  Conditional Expectation  Martingale  Stopping and Localizing  Martingale Convergence  L2-Martingales  Uniformly Integrable Martingales  Some Classical Results of Probability  Elementary Inequalities for Martingales  The Burkholder–Davis–Gundy Inequalities  Random Walks on ℤd – the first steps  Fluctuations of Simple Random Walks on Z Recurrence and Transience of General Random Walks Random Walks and Analysis Donsker's Invariance Principle and Brownian Motion","brand":"WoB","offers":[{"title":"US \/ NEW \/ INGRAM","offer_id":51061392408849,"sku":"NIN9783110350678","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52535255859473,"sku":"NLS9783110350678","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/311035067X.jpg?v=1751031312"},{"product_id":"ma-und-integral-book-ren-schilling-9783111342771","title":"Maß Und Integral","description":"\u003cp\u003eAllgemeine Maße und das Lebesgue-Integral gehören zu den unverzichtbaren Hilfsmitteln der modernen Analysis, der Funktionalanalysis und der Stochastik. Das vorliegende Lehrbuch bietet eine Einführung in die wesentlichen Aspekte der Theorie - Maße, Integrale, Konvergenzsätze, Parameterintegrale, Satz von Fubini -, die durch weiterführende Themen - allgemeiner Transformationssatz, Satz von Radon-Nikodým, Fouriertransformation von Maßen, topologische Maßtheorie - abgerundet wird. Mehr als 150 Übungsaufgaben (mit vollständigen Lösungen im Internet) vertiefen und erweitern den Stoff.\u003c\/p\u003e \u003cp\u003eDie kompakte Darstellung bietet sich als Fortsetzung der Grundvorlesungen \"Analysis\" oder als Einstieg in die \"Stochastik\" an. Da nur Grundkenntnisse in Analysis und linearer Algebra vorausgesetzt werden, ist der Text auch für Studierende der Physik und Ingenieurswissenschaften sowie zum Selbststudium geeignet.\u003c\/p\u003e \u003cp\u003eIn gleicher Ausstattung erscheinen die Folgebände \"Wahrscheinlichkeit\" und \"Martingale \u0026amp; Prozesse\".\u003c\/p\u003e \u003cp\u003eLösungen zu den im Buch befindlichen Übungsaufgaben unter: \u003ca href=\"http:\/\/www.motapa.de\/mint\/index.shtml\"\u003ehttp:\/\/www.motapa.de\/mint\/index.shtml\u003c\/a\u003e\u003c\/p\u003e","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51063128785169,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51063132586257,"sku":"NIN9783111342771","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3111342778.jpg?v=1750934799"},{"product_id":"brownian-motion-book-ren-schilling-9783110741254","title":"Brownian Motion","description":"Stochastic processes occur everywhere in the sciences, economics and engineering, and they need to be understood by (applied) mathematicians, engineers and scientists alike. This book gives a gentle introduction to Brownian motion and stochastic processes, in general. Brownian motion plays a special role, since it shaped the whole subject, displays most random phenomena while being still easy to treat, and is used in many real-life models. Im this new edition, much material is added, and there are new chapters on ''Wiener Chaos and Iterated Itô Integrals'' and ''Brownian Local Times''.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51064643453201,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51064645845265,"sku":"NIN9783110741254","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52482195390737,"sku":"NLS9783110741254","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3110741253.jpg?v=1751094490"},{"product_id":"bernstein-functions-book-ren-vondracek-9783110252293","title":"Bernstein Functions","description":"Bernstein functions appear in various fields of mathematics, e.g. probability theory, potential theory, operator theory, functional analysis and complex analysis – often with different definitions and under different names. Among the synonyms are `Laplace exponent' instead of Bernstein function, and complete Bernstein functions are sometimes called `Pick functions', `Nevanlinna functions' or `operator monotone functions'.   This monograph – now in its second revised and extended edition – offers a self-contained and unified approach to Bernstein functions and closely related function classes, bringing together old and establishing new connections. For the second edition the authors added a substantial amount of new material. As in the first edition Chapters 1 to 11 contain general material which should be accessible to non-specialists, while the later Chapters 12 to 15 are devoted to more specialized topics. An extensive list of complete Bernstein functions with their representations is provided.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51065527304465,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51065529172241,"sku":"NIN9783110252293","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3110252295.jpg?v=1751415784"},{"product_id":"measure-integral-probability-processes-book-ren-l-schilling-9798599104889","title":"Measure, Integral, Probability \u0026 Processes","description":null,"brand":"WoB","offers":[{"title":"GB \/ LIKE_NEW \/ INTERNAL","offer_id":52090210353425,"sku":"GOR014485259","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9798599104889.jpg?v=1756911849"}],"url":"https:\/\/www.worldofbooks.com\/en-gb\/collections\/author-books-by-ren-l-schilling.oembed","provider":"World of Books ","version":"1.0","type":"link"}