Overview

This volume presents a representative work of Chinese probabilists on probability theory and its applications in physics. Interesting results of jump Markov processes are discussed, as well as Markov interacting processes with noncompact states, including the Schlogal model taken from statistical physics. The main body of this book is self-contained and can be used in a course in stochastic processes for graduate students. The book consists of four parts. In Parts 1 and 2, the author introduces the general theory for jump processes. New contributions to the classical problems: uniqueness, recurrence and positive recurrence are studied. Then, probability metrics and coupling methods, stochastically monotonicity, reversibility, large deviations and the estimates of L squared-spectral gap are discussed. Part 3 begins with the study of equilibrium particle systems. This contains the criteria of the reversibility, the construction of Gibbs states and the particle systems on lattice fractals. The final part emphasizes the reaction-diffusion processes which come from non-equilibrium statistical physics. Topics include constructions, existence of stationary distributions, ergodicity, phase transitions and hydrodynamic limits for the processes.

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9789810206390

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"""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"

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

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