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Dirichlet forms and Markov processes
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ISBN: 0444854215 9780080954295 0080954294 1282618652 9786612618659 9780444854216 Year: 1980 Volume: 23 Publisher: Amsterdam : North-Holland Pub. Co.,

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This book provides a comprehensive introduction to modern global variational theory on fibred spaces. It is based on differentiation and integration theory of differential forms on smooth manifolds, and on the concepts of global analysis and geometry such as jet prolongations of manifolds, mappings, and Lie groups. The book will be invaluable for researchers and PhD students in differential geometry, global analysis, differential equations on manifolds, and mathematical physics, and for the readers who wish to undertake further rigorous study in this broad interdisciplinary field.


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Functional analysis in Markov processes
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ISBN: 354011484X 038711484X 354039155X 9783540114840 Year: 1982 Volume: 923 Publisher: Berlin: Springer,

Dirichlet forms and Markov processes
Author:
ISBN: 0444854215 9780080954295 0080954294 Year: 1980 Publisher: Amsterdam

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Abstract

This book provides a comprehensive introduction to modern global variational theory on fibred spaces. It is based on differentiation and integration theory of differential forms on smooth manifolds, and on the concepts of global analysis and geometry such as jet prolongations of manifolds, mappings, and Lie groups. The book will be invaluable for researchers and PhD students in differential geometry, global analysis, differential equations on manifolds, and mathematical physics, and for the readers who wish to undertake further rigorous study in this broad interdisciplinary field.


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Symmetric Markov Processes, Time Change, and Boundary Theory (LMS-35)
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ISBN: 9781400840564 9780691136059 Year: 2011 Publisher: Princeton, N.J. Princeton University Press

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Mathematics


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Symmetric Markov processes, time change, and boundary theory
Authors: ---
ISBN: 1283290944 9786613290946 9781283290944 Year: 2011 Publisher: Princeton, N.J. : Princeton University Press,

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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.

Keywords

Markov processes. --- Boundary value problems. --- Dirichlet problem. --- Beurling-Deny decomposition. --- Beurling-Deny formula. --- Brownian motions. --- Dirichlet forms. --- Dirichlet spaces. --- Douglas integrals. --- Feller measures. --- Hausdorff topological space. --- Markovian symmetric operators. --- Silverstein extension. --- additive functional theory. --- additive functionals. --- analytic concepts. --- analytic potential theory. --- boundary theory. --- countable boundary. --- decompositions. --- energy functional. --- extended Dirichlet spaces. --- fine properties. --- harmonic functions. --- harmonicity. --- hitting distributions. --- irreducibility. --- lateral condition. --- local properties. --- m-tight special Borel. --- many-point extensions. --- one-point extensions. --- part processes. --- path behavior. --- perturbed Dirichlet forms. --- positive continuous additive functionals. --- probabilistic derivation. --- probabilistic potential theory. --- quasi properties. --- quasi-homeomorphism. --- quasi-regular Dirichlet forms. --- recurrence. --- reflected Dirichlet spaces. --- reflecting Brownian motions. --- reflecting extensions. --- regular Dirichlet forms. --- regular recurrent Dirichlet forms. --- smooth measures. --- symmetric Hunt processes. --- symmetric Markov processes. --- symmetric Markovian semigroups. --- terminal random variables. --- time change theory. --- time changes. --- time-changed process. --- transience. --- transient regular Dirichlet forms.


Book
Symmetric Markov processes, time change, and boundary theory
Authors: ---
ISBN: 9781400840564 1400840562 9780691136059 069113605X Year: 2011 Publisher: Princeton, N.J. Princeton University Press

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Itô's stochastic calculus and probability theory
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ISBN: 4431701869 4431685340 4431685324 Year: 1996 Publisher: Tokyo Springer

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Dirichlet forms and symmetric Markov processes
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ISBN: 311011626X Year: 1994 Publisher: Berlin De Gruyter

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Dirichlet Forms and Symmetric Markov Processes
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ISBN: 9783110889741 Year: 2011 Publisher: Berlin Boston

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Digital
Dirichlet Forms and Symmetric Markov Processes
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ISBN: 9783110218091 9783110218084 Year: 2010 Publisher: Berlin ;; Boston De Gruyter

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Mathematics

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