eBook

Symmetric Markov processes, time change, and boundary theory

Fukushima, Masatoshi, Chen, Zhenqing

2011,2012

Overview

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.

• Publisher: Princeton University Press
• Subject: 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
• ISBN: 9780691136059, 069113605X, 9781400840564, 1400840562