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Author : M.L. Silverstein
Publisher : Springer
Page : 296 pages
File Size : 46,7 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540372929
Author : Zhen-Qing Chen,Masatoshi Fukushima
Publisher : Princeton University Press
Page : 496 pages
File Size : 44,5 Mb
Release : 2012
Category : Mathematics
ISBN : 9780691136059
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.
Author : Anonim
Publisher : Unknown
Page : 287 pages
File Size : 55,6 Mb
Release : 1964
Category : Markov processes
ISBN : 0387070125
Author : M.L. Silverstein
Publisher : Springer
Page : 329 pages
File Size : 52,9 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540382225
Author : Masatoshi Fukushima,Yoichi Oshima,Masayoshi Takeda
Publisher : Walter de Gruyter
Page : 501 pages
File Size : 47,5 Mb
Release : 2011
Category : Mathematics
ISBN : 9783110218084
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 revise
Author : Kai Lai Chung,John B. Walsh
Publisher : Springer Science & Business Media
Page : 444 pages
File Size : 48,8 Mb
Release : 2006-01-18
Category : Mathematics
ISBN : 9780387286969
From the reviews of the First Edition: "This excellent book is based on several sets of lecture notes written over a decade and has its origin in a one-semester course given by the author at the ETH, Zürich, in the spring of 1970. The author's aim was to present some of the best features of Markov processes and, in particular, of Brownian motion with a minimum of prerequisites and technicalities. The reader who becomes acquainted with the volume cannot but agree with the reviewer that the author was very successful in accomplishing this goal...The volume is very useful for people who wish to learn Markov processes but it seems to the reviewer that it is also of great interest to specialists in this area who could derive much stimulus from it. One can be convinced that it will receive wide circulation." (Mathematical Reviews) This new edition contains 9 new chapters which include new exercises, references, and multiple corrections throughout the original text.
Author : Tomasz Komorowski,Claudio Landim,Stefano Olla
Publisher : Springer Science & Business Media
Page : 494 pages
File Size : 50,5 Mb
Release : 2012-07-05
Category : Mathematics
ISBN : 9783642298806
The present volume contains the most advanced theories on the martingale approach to central limit theorems. Using the time symmetry properties of the Markov processes, the book develops the techniques that allow us to deal with infinite dimensional models that appear in statistical mechanics and engineering (interacting particle systems, homogenization in random environments, and diffusion in turbulent flows, to mention just a few applications). The first part contains a detailed exposition of the method, and can be used as a text for graduate courses. The second concerns application to exclusion processes, in which the duality methods are fully exploited. The third part is about the homogenization of diffusions in random fields, including passive tracers in turbulent flows (including the superdiffusive behavior). There are no other books in the mathematical literature that deal with this kind of approach to the problem of the central limit theorem. Hence, this volume meets the demand for a monograph on this powerful approach, now widely used in many areas of probability and mathematical physics. The book also covers the connections with and application to hydrodynamic limits and homogenization theory, so besides probability researchers it will also be of interest also to mathematical physicists and analysts.
Author : Anonim
Publisher : Unknown
Page : 313 pages
File Size : 51,6 Mb
Release : 1964
Category : Markov processes
ISBN : 0387076883
Author : Zhi-Ming Ma,Michael Röckner
Publisher : Springer Science & Business Media
Page : 215 pages
File Size : 51,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642777394
The purpose of this book is to give a streamlined introduction to the theory of (not necessarily symmetric) Dirichlet forms on general state spaces. It includes both the analytic and the probabilistic part of the theory up to and including the construction of an associated Markov process. It is based on recent joint work of S. Albeverio and the two authors and on a one-year-course on Dirichlet forms taught by the second named author at the University of Bonn in 1990/9l. It addresses both researchers and graduate students who require a quick but complete introduction to the theory. Prerequisites are a basic course in probabil ity theory (including elementary martingale theory up to the optional sampling theorem) and a sound knowledge of measure theory (as, for example, to be found in Part I of H. Bauer [B 78]). Furthermore, an elementary course on lin ear operators on Banach and Hilbert spaces (but without spectral theory) and a course on Markov processes would be helpful though most of the material needed is included here.
Author : Yoichi Oshima
Publisher : de Gruyter
Page : 0 pages
File Size : 43,6 Mb
Release : 2013
Category : Mathematics
ISBN : 3110302004
Symmetric Dirichlet forms andtheir associated Markov processes are important and powerful toolsin the theory of Markovprocesses and their applications. In this monograph, wegeneralize the theory to non-symmetric and time dependent semi-Dirichlet forms. Thus, we can cover the wide class of Markov processes and analytic theory which do not possess the dualMarkov processes.
Author : Yoichi Oshima
Publisher : Walter de Gruyter
Page : 296 pages
File Size : 47,8 Mb
Release : 2013-04-30
Category : Mathematics
ISBN : 9783110302066
This book deals with analytic treatments of Markov processes. Symmetric Dirichlet forms and their associated Markov processes are important and powerful tools in the theory of Markov processes and their applications. The theory is well studied and used in various fields. In this monograph, we intend to generalize the theory to non-symmetric and time dependent semi-Dirichlet forms. By this generalization, we can cover the wide class of Markov processes and analytic theory which do not possess the dual Markov processes. In particular, under the semi-Dirichlet form setting, the stochastic calculus is not well established yet. In this monograph, we intend to give an introduction to such calculus. Furthermore, basic examples different from the symmetric cases are given. The text is written for graduate students, but also researchers.
Author : Daniel W. Stroock
Publisher : Springer Science & Business Media
Page : 213 pages
File Size : 40,6 Mb
Release : 2013-10-28
Category : Mathematics
ISBN : 9783642405235
This book provides a rigorous but elementary introduction to the theory of Markov Processes on a countable state space. It should be accessible to students with a solid undergraduate background in mathematics, including students from engineering, economics, physics, and biology. Topics covered are: Doeblin's theory, general ergodic properties, and continuous time processes. Applications are dispersed throughout the book. In addition, a whole chapter is devoted to reversible processes and the use of their associated Dirichlet forms to estimate the rate of convergence to equilibrium. These results are then applied to the analysis of the Metropolis (a.k.a simulated annealing) algorithm. The corrected and enlarged 2nd edition contains a new chapter in which the author develops computational methods for Markov chains on a finite state space. Most intriguing is the section with a new technique for computing stationary measures, which is applied to derivations of Wilson's algorithm and Kirchoff's formula for spanning trees in a connected graph.
Author : Thomas Milton Liggett
Publisher : American Mathematical Soc.
Page : 290 pages
File Size : 51,5 Mb
Release : 2010
Category : Markov processes
ISBN : 9780821849491
Markov processes are among the most important stochastic processes for both theory and applications. This book develops the general theory of these processes, and applies this theory to various special examples.
Author : Niels Jacob
Publisher : Imperial College Press
Page : 506 pages
File Size : 54,9 Mb
Release : 2001
Category : Mathematics
ISBN : 9781860945687
This work covers two topics in detail: Fourier analysis, with emphasis on positivity and also on some function spaces and multiplier theorems; and one-parameter operator semigroups with emphasis on Feller semigroups and Lp-sub-Markovian semigroups. In addition, Dirichlet forms are treated.
Author : Kai Lai Chung
Publisher : World Scientific
Page : 124 pages
File Size : 40,5 Mb
Release : 1995
Category : Science
ISBN : 9810225334
This volume shows modern probabilistic methods in action: Brownian Motion Process as applied to the electrical phenomena investigated by Green et al., beginning with the Newton-Coulomb potential and ending with solutions by first and last exits of Brownian paths from conductors.