LEADER 04973nam 2200697Ia 450 001 9910814857803321 005 20240404154103.0 010 $a1-281-91956-X 010 $a9786611919566 010 $a981-277-460-2 035 $a(CKB)1000000000404593 035 $a(EBL)1681654 035 $a(OCoLC)879025564 035 $a(SSID)ssj0000211782 035 $a(PQKBManifestationID)11196122 035 $a(PQKBTitleCode)TC0000211782 035 $a(PQKBWorkID)10135414 035 $a(PQKB)11406806 035 $a(MiAaPQ)EBC1681654 035 $a(WSP)00005972 035 $a(Au-PeEL)EBL1681654 035 $a(CaPaEBR)ebr10201388 035 $a(CaONFJC)MIL191956 035 $a(PPN)168028808 035 $a(EXLCZ)991000000000404593 100 $a20061012d2006 uu 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aNon-autonomous Kato classes and Feynman-Kac propagators /$fArchil Gulisashvili, Jan A. van Casteren 205 $a1st ed. 210 $aSingapore ;$aHackensack, N.J. $cWorld Scientific$d2006 215 $a1 online resource (360 p.) 300 $aDescription based upon print version of record. 311 $a981-256-557-4 320 $aIncludes bibliographical references and index. 327 $aContents ; 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 Property 327 $a1.3 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-Algebras 327 $a1.8 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 Processes 327 $a1.12 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 Theory 327 $a2.1 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 Semigroups 327 $a2.5 Feller-Dynkin Propagators and the Continuity Properties of Markov Processes 330 $a 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 pre 606 $aLinear operators 606 $aBanach spaces 606 $aOperator theory 615 0$aLinear operators. 615 0$aBanach spaces. 615 0$aOperator theory. 676 $a530.15 700 $aGulisashvili$b Archil$01602380 701 $aCasteren$b J. A. van$0149912 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910814857803321 996 $aNon-autonomous Kato classes and Feynman-Kac propagators$93926342 997 $aUNINA