This book gives a comprehensive and self-contained introduction to the theory of symmetric Markov processes and symmetric quasi-regular Dirichlet forms. In a detailed and accessible manner, Zhen-Qing Chen and Masatoshi Fukushima cover the essential elements and applications of the theory of symmetric Markov processes, including recurrence/transience criteria, probabilistic potential theory, additive functional theory, and time change theory. The authors develop the theory in a general framework of symmetric quasi-regular Dirichlet forms in a unified manner with that of regular Dirichlet forms, emphasizing the role of extended Dirichlet spaces and the rich interplay between the probabilistic and analytic aspects of the theory. Chen and Fukushima then address the latest advances in the theory, presented here for the first time in any book. Topics include the characterization of time-changed Markov processes in terms of Douglas integrals and a systematic account of reflected Dirichlet spaces, and the important roles such advances play in the boundary theory of symmetric Markov processes.
 This volume is an ideal resource for researchers and practitioners, and can also serve as a textbook for advanced graduate students. It includes examples, appendixes, and exercises with solutions.

Symmetric Markov Processes, Time Change, and Boundary Theory (LMS-35) (London Mathematical Society Monographs)

Science & Math

Fukushima, Masatoshi

Chen, Zhenqing

Mathematics

Princeton University Press

Since the publication of the first edition in 1994, this book has attracted constant interests from readers and is by now regarded as a standard reference for the theory of Dirichlet forms. For the present second edition, the authors not only revised the existing text, but also added some new sections as well as several exercises with solutions. The book addresses to researchers and graduate students who wish to comprehend the area of Dirichlet forms and symmetric Markov processes.

Dirichlet Forms and Symmetric Markov Processes (Degruyter Studies in Mathematics)

de Gruyter

Dirichlet Forms and Symmetric Markov Processes (de Gruyter Studies in Mathematics, Vol. 19) (De Gruyter Studies in Mathematics, 19)

Oshima, Yoichi

Takeda, Masayoshi

Walter de Gruyter

Professor Kiyosi Ito is well known as the creator of the modern theory of stochastic analysis. Although Ito first proposed his theory, now known as Ito's stochastic analysis or Ito's stochastic calculus, about fifty years ago, its value in both pure and applied mathematics is becoming greater and greater. For almost all modern theories at the forefront of probability and related fields, Ito's analysis is indispensable as an essential instrument, and it will remain so in the future. For example, a basic formula, called the Ito formula, is well known and widely used in fields as diverse as physics and economics. This volume contains 27 papers written by world-renowned probability theorists. Their subjects vary widely and they present new results and ideas in the fields where stochastic analysis plays an important role. Also included are several expository articles by well-known experts surveying recent developments. Not only mathematicians but also physicists, biologists, economists and researchers in other fields who are interested in the effectiveness of stochastic theory will find valuable suggestions for their research. In addition, students who are beginning their study and research in stochastic analysis and related fields will find instructive and useful guidance here. This volume is dedicated to Professor Ito on the occasion of his eightieth birthday as a token of deep appreciation for his great achievements and contributions. An introduction to and commentary on the scientific works of Professor Ito are also included.

Itô’s Stochastic Calculus and Probability Theory

Crafts, Hobbies & Home

Kunita, Hiroshi

Ikeda, Nobuyuki

Watanabe, Sinzo

Gardening & Landscape Design

Springer

Stochastic Komatu-Loewner Evolutions

Chen, Zhen-Qing

Murayama, Takuya

Evolution

World Scientific Pub Co Inc

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