06325nam 2201393 a 450 991078972490332120220310020504.01-283-29094-4978661329094610.1515/9781400840564(CKB)2670000000121262(EBL)784514(OCoLC)758507199(SSID)ssj0000593286(PQKBManifestationID)11353928(PQKBTitleCode)TC0000593286(PQKBWorkID)10740629(PQKB)10796810(MiAaPQ)EBC784514(StDuBDS)EDZ0000406838(WaSeSS)Ind00024835(DE-B1597)447016(OCoLC)979579452(DE-B1597)9781400840564(Au-PeEL)EBL784514(CaPaEBR)ebr10503233(CaONFJC)MIL329094(PPN)19924460X(PPN)187958378(EXLCZ)99267000000012126220110719d2011 uy 0engurnn#---uu||utxtccrSymmetric Markov processes, time change, and boundary theory[electronic resource] /Zhen-Qing Chen, Masatoshi FukushimaCourse BookPrinceton, N.J. Princeton University Press20111 online resource (496 p.)London Mathematical Society monographs ;v. 35Description based upon print version of record.0-691-13605-X 1-4008-4056-2 Includes bibliographical references and index.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 --IndexThis 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.London Mathematical Society monographs ;v. 35.Markov processesBoundary value problemsDirichlet problemBeurling-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.Markov processes.Boundary value problems.Dirichlet problem.519.233Chen Zhen-Qing514801Fukushima Masatoshi55765MiAaPQMiAaPQMiAaPQBOOK9910789724903321Symmetric Markov processes, time change, and boundary theory850816UNINA