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The Resource Boundary value problems and Markov processes, Kazuaki Taira, (electronic book)

Boundary value problems and Markov processes, Kazuaki Taira, (electronic book)

Label
Boundary value problems and Markov processes
Title
Boundary value problems and Markov processes
Statement of responsibility
Kazuaki Taira
Creator
Subject
Language
eng
Summary
Annotation
Member of
Cataloging source
GW5XE
http://library.link/vocab/creatorName
Taira, Kazuaki
Dewey number
515/.35
Illustrations
illustrations
Index
index present
LC call number
  • QA379
  • QA3
LC item number
  • .T35 2009
  • .L28 no.1499 2009
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
Series statement
Lecture notes in mathematics,
Series volume
1499
http://library.link/vocab/subjectName
  • Boundary value problems
  • Differential equations, Elliptic
  • Markov processes
Summary expansion
This 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
Label
Boundary value problems and Markov processes, Kazuaki Taira, (electronic book)
Instantiates
Publication
Note
"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
Bibliography note
Includes bibliographical references (p. 179-182) and index
Control code
SPR432702845
Dimensions
unknown
Edition
2nd ed.
Extent
1 online resource (xii, 186 p.)
Form of item
online
Isbn
9783642016776
Other physical details
ill.
Specific material designation
remote
Label
Boundary value problems and Markov processes, Kazuaki Taira, (electronic book)
Publication
Note
"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
Bibliography note
Includes bibliographical references (p. 179-182) and index
Control code
SPR432702845
Dimensions
unknown
Edition
2nd ed.
Extent
1 online resource (xii, 186 p.)
Form of item
online
Isbn
9783642016776
Other physical details
ill.
Specific material designation
remote

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