On the existence of Feller semigroups with boundary conditions
About this Title
Publication: Memoirs of the American Mathematical Society
Publication Year 1992: Volume 99, Number 475
ISBNs: 978-0-8218-2535-8 (print); 978-1-4704-0901-2 (online)
MathSciNet review: 1120243
MSC (1991): Primary 47D07; Secondary 35J25, 47N20, 60J25
This monograph provides a careful and accessible exposition of functional analytic methods in stochastic analysis. The author focuses on the relationship among three subjects in analysis: Markov processes, Feller semigroups, and elliptic boundary value problems. The approach here is distinguished by the author's extensive use of the theory of partial differential equations. Filling a mathematical gap between textbooks on Markov processes and recent developments in analysis, this work describes a powerful method capable of extensive further development. The book would be suitable as a textbook in a one-year, advanced graduate course on functional analysis and partial differential equations, with emphasis on their strong interrelations with probability theory.
Mathematicians and graduate students working in functional analysis, partial differential equations and probability; graduate students about to enter the subject; and mathematicians in the field looking for a coherent overview.
Table of Contents
- Introduction and results
- I. Theory of Feller semigroups
- II. Theory of pseudo-differential operators
- III. Proof of Theorem 1
- IV. Proof of Theorem 2
- Appendix. The maximum principle