Semigoups, Boundary Value Problems and Markov Processes
(Sprache: Englisch)
This volume will be of great appeal to both advanced students and researchers. For the former, it serves as an effective introduction to three interrelated subjects of analysis: semigroups, Markov processes and elliptic boundary value problems. For the...
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This volume will be of great appeal to both advanced students and researchers. For the former, it serves as an effective introduction to three interrelated subjects of analysis: semigroups, Markov processes and elliptic boundary value problems. For the latter, it provides a new method for the analysis of Markov processes, a powerful method clearly capable of extensive further development.
Klappentext zu „Semigoups, Boundary Value Problems and Markov Processes “
The purpose of this book is to provide a careful and accessible account along modern lines of the subject which the title deals, as well as to discuss problems of current interest in the field. More precisely this book is devoted to the functional-analytic approach to a class of degenerate boundary value problems for second-order elliptic integro-differential operators which includes as particular cases the Dirichlet and Robin problems. This class of boundary value problems provides a new example of analytic semigroups. As an application, we construct a strong Markov process corresponding to such a diffusion phenomenon that 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.
Inhaltsverzeichnis zu „Semigoups, Boundary Value Problems and Markov Processes “
Preface- Introduction and Main Results
- Theory of Semigroups
- Markov Processes and Semigroups
- Theory of Distributions
- Theory of Pseudo-Differential Operators
- Appendix A Boundedness of Pseudo-Differential Operators
- Elliptic Boundary Value Problems
- Elliptic Boundary Value Problems and Feller Semigroups
- Appendix B Unique Solvability of Pseudo-Differential Operators
- Proof of Theorem 1
- Proof of Theorem 2
- A Priori Estimates
- Proof of Theorem 3
- Proof of Theorem 4, Part (i)
- Proofs of Theorem 5 and Theorem 4, Part (ii)
- Boundary Value Problems for Waldenfels Operators
- Appendix C The Maximum Principle
- Bibliography
- Index of Symbols
- Subject Index.
Autoren-Porträt von K. Taira
Kazuaki TAIRA is Professor of Mathematics at the University of Tsukuba, Japan, where he has taught since 1998. He received his Bachelor of Science (1969) degree from the University of Tokyo, Japan, and his Master of Science (1972) degree from Tokyo Institute of Technology, Japan, where he served as an Assistant.
Bibliographische Angaben
- Autor: K. Taira
- 2004, 352 Seiten, Maße: 15,5 x 23,5 cm, Gebunden, Englisch
- Verlag: Springer, Berlin
- ISBN-10: 3540406514
- ISBN-13: 9783540406518
- Erscheinungsdatum: 07.10.2003
Sprache:
Englisch
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