Symmetric Markov processes, time change, and boundary theory

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 symmetri...

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Hauptverfasser:	Chen, Zhenqing, Fukushima, Masatoshi
Format:	E-Book Buch
Sprache:	Englisch
Veröffentlicht:	Princeton Princeton University Press 2011
Ausgabe:	1
Schriftenreihe:	London Mathematical Society monographs
Schlagworte:	Absolute continuity Bilinear form Borel right process Borel set Boundary value problems Brownian motion Cauchy process Characterization (mathematics) Compact space Constant function Continuous function Continuous function (set theory) Corollary Diffusion process Dimension Dirichlet integral Division by zero Equation Equivalence class Existence theorem Existential quantification Fatou's lemma Fourier transform Fubini's theorem Function (mathematics) Function space Harmonic function Hilbert space Homeomorphism Identity matrix Infinitesimal generator (stochastic processes) Interest Interval (mathematics) Irreducibility (mathematics) Lebesgue measure Linear map Lipschitz continuity Lipschitz domain London Mathematical Society Markov chain Markov process Markov processes Markov property Martingale (probability theory) MATHEMATICS MATHEMATICS / Probability & Statistics / General Measurable function Measure (mathematics) Monotonic function Open set Oxford University Press Poisson point process Potential theory Princeton University Press Probability Probability measure Radon measure Riemannian manifold Rotational symmetry Self-adjoint operator Semigroup Semimartingale Sign (mathematics) Sobolev space Special case Statistics Stochastic calculus Stochastic differential equation Stochastic process Subset Summation Theorem Theory Transition function Constant function Open set Measurable function Subset Identity matrix Function space Fatou's lemma Stochastic process Interest Self-adjoint operator Infinitesimal generator (stochastic processes) Martingale (probability theory) Characterization (mathematics) Hilbert space Semimartingale Corollary Monotonic function Radon measure Absolute continuity Lipschitz domain Existence theorem Semigroup Continuous function Fubini's theorem Riemannian manifold Function (mathematics) Bilinear form Harmonic function Existential quantification Brownian motion Division by zero Poisson point process Homeomorphism Borel right process Special case Summation Probability measure Markov process Sign (mathematics) Continuous function (set theory) Equivalence class Sobolev space Theory Rotational symmetry Dirichlet integral Fourier transform Potential theory Mathematics London Mathematical Society Interval (mathematics) Lipschitz continuity Markov chain Lebesgue measure Linear map Diffusion process Oxford University Press Cauchy process Theorem Stochastic differential equation Transition function Markov property Compact space Borel set Probability Equation Dimension Princeton University Press Stochastic calculus Measure (mathematics) Irreducibility (mathematics)
ISBN:	9780691136059, 069113605X, 9781400840564, 1400840562
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	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.
Bibliographie:	Includes bibliographical reference (p. [457]-466) and index
ISBN:	9780691136059 069113605X 9781400840564 1400840562
DOI:	10.1515/9781400840564