Memoirs of the American Mathematical Society 1992; 65 pp; softcover Volume: 99 ISBN10: 0821825356 ISBN13: 9780821825358 List Price: US$28 Individual Members: US$16.80 Institutional Members: US$22.40 Order Code: MEMO/99/475
 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 oneyear, 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 pseudodifferential operators
 Proof of Theorem 1
 Proof of Theorem 2
 Appendix the maximum principle
