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Semigroups, boundary value problems, and Markov processes / Kazuaki Taira.

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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 ellipt...

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Bibliographic Details
Online Access: Full Text (via Springer)
Main Author: Taira, Kazuaki (Author)
Format: eBook
Language:English
Published: Berlin : Springer, [2014]
Edition:Second edition.
Series:Springer monographs in mathematics.
Subjects:
Markov processes.
Semigroups.
Boundary value problems.
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.

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