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.

Readership

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
• Theory of Feller semigroups
• Theory of pseudo-differential operators
• Proof of Theorem 1
• Proof of Theorem 2
• Appendix the maximum principle