Semigroups, boundary value problems, and Markov processes /

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Bibliographic Details
Author / Creator:	Taira, Kazuaki, author.
Edition:	Second edition.
Imprint:	Berlin : Springer, [2014] ©2014
Description:	1 online resource (xix, 716 pages) : illustrations.
Language:	English
Series:	Springer monographs in mathematics, 1439-7382 Springer monographs in mathematics.
Subject:	Markov processes. Semigroups. Boundary value problems. Boundary value problems. Markov processes. Semigroups. MATHEMATICS -- Applied. MATHEMATICS -- Probability & Statistics -- General. Boundary value problems. Markov processes. Semigroups. Elliptisches Randwertproblem. Analytische Halbgruppe. Markov-Prozess. Electronic books.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11086944

Hidden Bibliographic Details
ISBN:	9783662436967 3662436965 3662436957 9783662436950 9783662436950
Notes:	Includes bibliographical references and index. Online resource; title from PDF title page (SpringerLink, viewed Aug. 14, 2014).
Summary:	A careful and accessible exposition of functional analytic methods in stochastic analysis is provided in this book. It focuses on the interrelationship between three subjects in analysis: Markov processes, semi groups and elliptic boundary value problems. The author studies a general class of elliptic boundary value problems for second-order, Waldenfels integro-differential operators in partial differential equations and proves that this class of elliptic boundary value problems provides a general class of Feller semigroups in functional analysis. As an application, the author constructs a general class of Markov processes in probability in which a Markovian particle moves both by jumps and continuously in the state space until it 'dies' at the time when it reaches the set where the particle is definitely absorbed. Augmenting the 1st edition published in 2004, this edition includes four new chapters and eight re-worked and expanded chapters. It is amply illustrated and all chapters are rounded off with Notes and Comments where bibliographical references are primarily discussed. Thanks to the kind feedback from many readers, some errors in the first edition have been corrected. In order to keep the book up-to-date, new references have been added to the bibliography. Researchers and graduate students interested in PDEs, functional analysis and probability will find this volume useful.
Other form:	Printed edition: 9783662436950
Standard no.:	10.1007/978-3-662-43696-7

Table of Contents:

1. Introduction and Main Results
Part I Elements of Analysis
2. Elements of Probability Theory
3. Elements of Functional Analysis
4. Theory of Semigroups
Part II Elements of Partial Differential Equations
5. Theory of Distributions
6. Sobolev and Besov Spaces
7. Theory of Pseudo-Differential Operators
8. Waldenfels Operators and Maximum Principles
Part III Markov Processes, Semigroups and Boundary Value problems
9. Markov Processes, Transition Functions and Feller Semigroups
10. Feller Semigroups and Elliptic Boundary Value Problems
11. Proof of Theorem 1.3
12. Markov Processes Revisited
13. Concluding Remarks
Appendix: Boundedness of Pseudo-Differential Operators
References
Index.

Semigroups, boundary value problems, and Markov processes /

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