LEADER 05198nam 22007095 450 001 9910483698803321 005 20200704091129.0 010 $a1-280-38434-4 010 $a9786613562265 010 $a3-642-01677-4 024 7 $a10.1007/978-3-642-01677-6 035 $a(CKB)1000000000753943 035 $a(SSID)ssj0000316535 035 $a(PQKBManifestationID)11246840 035 $a(PQKBTitleCode)TC0000316535 035 $a(PQKBWorkID)10275225 035 $a(PQKB)10497028 035 $a(DE-He213)978-3-642-01677-6 035 $a(MiAaPQ)EBC3064299 035 $a(PPN)136306330 035 $a(EXLCZ)991000000000753943 100 $a20100301d2009 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aBoundary Value Problems and Markov Processes$b[electronic resource] /$fby Kazuaki Taira 205 $a2nd ed. 2009. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2009. 215 $a1 online resource (XII, 192 p. 41 illus.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1499 300 $a"This second edition has been revised to streamline some of the analysis and to give better coverage of important examples and applications. The errors in the first printing are corrected ... additional references have been included in the bibliography."--p. vii. 311 $a3-642-01676-6 320 $aIncludes bibliographical references (p. 179-182) and index. 327 $aand Main Results -- Semigroup Theory -- L Theory of Pseudo-Differential Operators -- L Approach to Elliptic Boundary Value Problems -- Proof of Theorem 1.1 -- A Priori Estimates -- Proof of Theorem 1.2 -- Proof of Theorem 1.3 - Part (i) -- Proof of Theorem 1.3, Part (ii) -- Application to Semilinear Initial-Boundary Value Problems -- Concluding Remarks. 330 $aThis volume is devoted to a thorough and accessible exposition on the functional analytic approach to the problem of construction of Markov processes with Ventcel' boundary conditions in probability theory. Analytically, a Markovian particle in a domain of Euclidean space is governed by an integro-differential operator, called a Waldenfels operator, in the interior of the domain, and it obeys a boundary condition, called the Ventcel' boundary condition, on the boundary of the domain. Probabilistically, a Markovian particle moves both by jumps and continuously in the state space and it obeys the Ventcel' boundary condition, which consists of six terms corresponding to the diffusion along the boundary, the absorption phenomenon, the reflection phenomenon, the sticking (or viscosity) phenomenon, the jump phenomenon on the boundary, and the inward jump phenomenon from the boundary. In particular, second-order elliptic differential operators are called diffusion operators and describe analytically strong Markov processes with continuous paths in the state space such as Brownian motion. We observe that second-order elliptic differential operators with smooth coefficients arise naturally in connection with the problem of construction of Markov processes in probability. Since second-order elliptic differential operators are pseudo-differential operators, we can make use of the theory of pseudo-differential operators as in the previous book: Semigroups, boundary value problems and Markov processes (Springer-Verlag, 2004). Our approach here is distinguished by its extensive use of the ideas and techniques characteristic of the recent developments in the theory of partial differential equations. Several recent developments in the theory of singular integrals have made further progress in the study of elliptic boundary value problems and hence in the study of Markov processes possible. The presentation of these new results is the main purpose of this book. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1499 606 $aMathematical analysis 606 $aAnalysis (Mathematics) 606 $aPartial differential equations 606 $aOperator theory 606 $aProbabilities 606 $aAnalysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12007 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aOperator Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M12139 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 615 0$aMathematical analysis. 615 0$aAnalysis (Mathematics). 615 0$aPartial differential equations. 615 0$aOperator theory. 615 0$aProbabilities. 615 14$aAnalysis. 615 24$aPartial Differential Equations. 615 24$aOperator Theory. 615 24$aProbability Theory and Stochastic Processes. 676 $a519.233 700 $aTaira$b Kazuaki$4aut$4http://id.loc.gov/vocabulary/relators/aut$059537 906 $aBOOK 912 $a9910483698803321 996 $aBoundary value problems and Markov processes$978656 997 $aUNINA