Symmetric Markov processes, time change, and boundary theory / / Zhen-Qing Chen, Masatoshi Fukushima

• Autore: Chen Zhen-Qing
• Pubblicazione: Princeton, N.J., : Princeton University Press, 2011
• Edizione: Course Book
• Descrizione fisica: 1 online resource (496 p.)
• Disciplina: 519.233
• Soggetto topico: Markov processes; Boundary value problems; Dirichlet problem
• Soggetto non controllato: Beurling-Deny decomposition; Beurling-Deny formula; Brownian motions; Dirichlet forms; Dirichlet spaces; Douglas integrals; Feller measures; Hausdorff topological space; Markov processes; 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
• Altri autori: FukushimaMasatoshi
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Front matter -- Contents -- Notation -- Preface -- Chapter One. Symmetric Markovian Semigroups and Dirichlet Forms -- Chapter Two. Basic Properties and Examples of Dirichlet Forms -- Chapter Three. Symmetric Hunt Processes and Regular Dirichlet Forms -- Chapter Four. Additive Functionals of Symmetric Markov Processes -- Chapter Five. Time Changes of Symmetric Markov Processes -- Chapter Six. Reflected Dirichlet Spaces -- Chapter Seven. Boundary Theory for Symmetric Markov Processes -- Appendix A. Essentials of Markov Processes -- Appendix B. Solutions To Exercises -- Notes -- Bibliography -- Catalogue Of Some Useful Theorems -- Index
• Sommario/riassunto: 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.
• Titolo autorizzato: Symmetric Markov processes, time change, and boundary theory
• ISBN: 1-283-29094-4; 9786613290946
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910820086603321
• Lo trovi qui: Univ. Federico II
• Serie: London Mathematical Society monographs ; ; v. 35.