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020 _a9783642016776
_9978-3-642-01677-6
024 7 _a10.1007/978-3-642-01677-6
_2doi
050 4 _aQA299.6-433
072 7 _aPBK
_2bicssc
072 7 _aMAT034000
_2bisacsh
072 7 _aPBK
_2thema
082 0 4 _a515
_223
100 1 _aTaira, Kazuaki.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aBoundary Value Problems and Markov Processes
_h[electronic resource] /
_cby Kazuaki Taira.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2009.
300 _aXII, 192 p. 41 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1499
505 0 _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.
520 _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.
650 0 _aGlobal analysis (Mathematics).
650 0 _aDifferential equations, partial.
650 0 _aOperator theory.
650 0 _aDistribution (Probability theory.
650 1 4 _aAnalysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12007
650 2 4 _aPartial Differential Equations.
_0http://scigraph.springernature.com/things/product-market-codes/M12155
650 2 4 _aOperator Theory.
_0http://scigraph.springernature.com/things/product-market-codes/M12139
650 2 4 _aProbability Theory and Stochastic Processes.
_0http://scigraph.springernature.com/things/product-market-codes/M27004
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642023712
776 0 8 _iPrinted edition:
_z9783642016769
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1499
856 4 0 _uhttps://doi.org/10.1007/978-3-642-01677-6
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c9917
_d9917