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Some very new results are included, such as the estimate of the spectral gap. The structure and proofs in the first part are rather different from other existing textbooks on Markov chains.In the part on stochastic analysis, we cover the martingale theory and Brownian motions, the stochastic integral and stochastic differential equations with emphasis on one dimension, and the multidimensional stochastic integral and stochastic equation based on semimartingales. We introduce three important topics here: the Feynman-Kac formula, random time transform and Girsanov transform. As an essential application of the probability theory in classical mathematics, we also deal with the famous Brunn-Minkowski inequality in convex geometry.This volume also features modern probability theory that is used in the non-random fields, such as MCMC, convex geometry and number theory. It provides a new and direct routine for students going through the classical Markov chains to the modern stochastic analysis. It employs more modern techniques, such as coupling and duality, and functional inequalities with Dirichlet form.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51253013676305,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51253014528273,"sku":"NIN9789814740302","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52532393312529,"sku":"NLS9789814740302","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9814740306.jpg?v=1751320086"},{"product_id":"from-markov-chains-to-non-equilibrium-particle-systems-2nd-edition-book-mu-fa-chen-9789812388117","title":"FROM MARKOV CHAINS TO NON-EQUILIBRIUM PARTICLE SYSTEMS (2ND EDITION)","description":"This book is representative of the work of Chinese probabilists on probability theory and its applications in physics. It presents a unique treatment of general Markov jump processes: uniqueness, various types of ergodicity, Markovian couplings, reversibility, spectral gap, etc. It also deals with a typical class of non-equilibrium particle systems, including the typical Schl gl model taken from statistical physics. The constructions, ergodicity and phase transitions for this class of Markov interacting particle systems, namely, reaction-diffusion processes, are presented. In this new edition, a large part of the text has been updated and two-and-a-half chapters have been rewritten. The book is self-contained and can be used in a course on stochastic processes for graduate students.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52451509174545,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52451509764369,"sku":"NLS9789812388117","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9789812388117.jpg?v=1759361770"},{"product_id":"eigenvalues-inequalities-and-ergodic-theory-book-mu-fa-chen-9781849969383","title":"Eigenvalues, Inequalities, and Ergodic Theory","description":"The first and only book to make this research available in the West   Concise and accessible: proofs and other technical matters are kept to a minimum to help the non-specialist             Each chapter is self-contained to make the book easy-to-use","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52480479789329,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52480481231121,"sku":"NLS9781849969383","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781849969383.jpg?v=1785990257"},{"product_id":"eigenvalues-inequalities-and-ergodic-theory-book-mu-fa-chen-9781852338688","title":"Eigenvalues, Inequalities, and Ergodic Theory","description":"A problem of broad interest - the estimation of the spectral gap for matrices or differential operators (Markov chains or diffusions) - is covered in this book.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52535571939601,"sku":"NLS9781852338688","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":52755429130513,"sku":"NIN9781852338688","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781852338688.jpg?v=1785906349"},{"product_id":"from-markov-chains-to-non-equilibrium-particle-systems-book-m-f-chen-9789810206390","title":"FROM MARKOV CHAINS TO NON-EQUILIBRIUM PARTICLE SYSTEMS","description":"This volume is representative of the work of Chinese probabilitists on probability theory and its applications in physics. Many interesting results of Jump Markov Processes are discussed, and a very fashionable new class of Markov processes — Markov interacting processes with noncompact states, including the important Schlögl model taken from statistical physics, is also considered. The main body of this book is self-contained and can be used in a course on “Stochastic Processes” for graduate students.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52618339123473,"sku":"NLS9789810206390","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9789810206390.jpg?v=1761532858"}],"url":"https:\/\/www.worldofbooks.com\/collections\/author-books-by-mu-fa-chen.oembed","provider":"World of Books ","version":"1.0","type":"link"}