Author: Mu-Fa Chen
Publisher: World Scientific
Published: 2004-03-23
Total Pages: 612
ISBN-13: 9814482900
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' 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 Schlögl 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. Contents:An Overview of the Book: Starting from Markov ChainsGeneral Jump Processes:Transition Function and Its Laplace TransformExistence and Simple Constructions of Jump ProcessesUniqueness CriteriaRecurrence, Ergodicity and Invariant MeasuresProbability Metrics and Coupling MethodsSymmetrizable Jump Processes:Symmetrizable Jump Processes and Dirichlet FormsField TheoryLarge DeviationsSpectral GapEquilibrium Particle Systems:Random FieldsReversible Spin Processes and Exclusion ProcessesYang–Mills Lattice FieldNon-Equilibrium Particle Systems:Constructions of the ProcessesExistence of Stationary Distributions and ErgodicityPhase TransitionsHydrodynamic Limits Readership: Upper-level undergraduates, graduate students and researchers in mathematical physics, probability and statistics. Keywords:Jump Process;Reversible Jump Process;Spectral Gap;Coupling Method;Large Deviation;Random Field;Reaction-Diffusion Process;Hydrodynamic LimitReviews:“… this book should be very useful to anyone interested in Markov processes, because it can serve as an introduction to a large variety of subjects and models, as well as an account of some recent works of Chinese probabilists.”Mathematical Reviews Reviews of the First Edition: “More recently, the school led by the author in Beijing has worked on the construction and ergodic theory of the class of interacting particle systems known as reaction diffusion processes … This book provides a useful account of a substantial portion of the work of Chinese probabilists over the past two decades, much of which has been relatively inaccessible to Western workers … this is a useful reference work for probabilists working in these areas, and a contribution to international communication in probability theory.”Mathematical Reviews “The book is a comprehensive account of the theory of jump processes and particle systems. The author is an outstanding Chinese specialist in probability theory and stochastic processes creating the Chinese school of Markov processes.”Zentralblatt fur Mathematik “He did a lot to popularize the subject in China and with Yan Shi-Jian was instrumental in having the second special year 1988–89 at the Nankai Institute devoted to probability … The book is admirable not only for the circumstances in which it is written but for what it contains … Chen's book contains a wide variety of topics that cannot be found in any other place … if you are curious about interacting particle systems this book belongs on your bookshelf.”SIAM Reviews '
