04973nam 2200697Ia 450 991081485780332120240404154103.01-281-91956-X9786611919566981-277-460-2(CKB)1000000000404593(EBL)1681654(OCoLC)879025564(SSID)ssj0000211782(PQKBManifestationID)11196122(PQKBTitleCode)TC0000211782(PQKBWorkID)10135414(PQKB)11406806(MiAaPQ)EBC1681654(WSP)00005972(Au-PeEL)EBL1681654(CaPaEBR)ebr10201388(CaONFJC)MIL191956(PPN)168028808(EXLCZ)99100000000040459320061012d2006 uu 0engur|n|---|||||txtccrNon-autonomous Kato classes and Feynman-Kac propagators /Archil Gulisashvili, Jan A. van Casteren1st ed.Singapore ;Hackensack, N.J. World Scientific20061 online resource (360 p.)Description based upon print version of record.981-256-557-4 Includes bibliographical references and index.Contents ; Preface ; 1. Transition Functions and Markov Processes ; 1.1 Introduction ; 1.1.1 Notation ; 1.1.2 Elements of Probability Theory ; 1.1.3 Locally Compact Spaces ; 1.1.4 Stochastic Processes ; 1.1.5 Filtrations ; 1.2 Markov Property1.3 Transition Functions and Backward Transition Functions 1.4 Markov Processes Associated with Transition Functions ; 1.5 Space-Time Processes ; 1.6 Classes of Stochastic Processes ; 1.7 Completions of o-Algebras1.8 Path Properties of Stochastic Processes: Separability and Progressive Measurability 1.9 Path Properties of Stochastic Processes: One-Sided Continuity and Continuity ; 1.10 Reciprocal Transition Functions and Reciprocal Processes ; 1.11 Path Properties of Reciprocal Processes1.12 Examples of Transition Functions and Markov Processes 1.12.1 Brownian motion and Brownian bridge ; 1.12.2 Cauchy process and Cauchy bridge ; 1.12.3 Forward Kolmogorov representation of Brownian bridges ; 1.13 Notes and Comments ; 2. Propagators: General Theory2.1 Propagators and Backward Propagators on Banach Spaces 2.2 Free Propagators and Free Backward Propagators ; 2.3 Generators of Propagators and Kolmogorov's Forward and Backward Equations ; 2.4 Howland Semigroups2.5 Feller-Dynkin Propagators and the Continuity Properties of Markov Processes This book provides an introduction to propagator theory. Propagators, or evolution families, are two-parameter analogues of semigroups of operators. Propagators are encountered in analysis, mathematical physics, partial differential equations, and probability theory. They are often used as mathematical models of systems evolving in a changing environment. A unifying theme of the book is the theory of Feynman-Kac propagators associated with time-dependent measures from non-autonomous Kato classes. In applications, a Feynman-Kac propagator describes the evolution of a physical system in the preLinear operatorsBanach spacesOperator theoryLinear operators.Banach spaces.Operator theory.530.15Gulisashvili Archil1602380Casteren J. A. van149912MiAaPQMiAaPQMiAaPQBOOK9910814857803321Non-autonomous Kato classes and Feynman-Kac propagators3926342UNINA