On the existence of Feller semigroups with boundary conditions / Kazuaki Taira.

Format:

Book

Author/Creator:

Taira, Kazuaki, author.

Series:

Memoirs of the American Mathematical Society ; Volume 99, Number 475.

Memoirs of the American Mathematical Society, 0065-9266 ; Volume 99, Number 475

Language:

English

Subjects (All):

Markov processes.

Differential equations, Elliptic.

Boundary value problems.

Physical Description:

1 online resource (81 p.)

Edition:

1st ed.

Other Title:

Feller semigroups with boundary conditions.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 1992.

Language Note:

English

Summary:

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.

Contents:

""Table of Contents""; ""Abstract""; ""Acknowledgments""; ""Introduction and Results""; ""Chapter I. Theory of Feller Semigroups""; ""1.1 Markov Transition Functions and Feller Semigroups""; ""1.2 Generation Theorems of Feller Semigroups""; ""Chapter II. Theory of Pseudo-Differential Operators""; ""2.1 Function Spaces""; ""2.2 Pseudo-Differential Operators""; ""2.3 Unique Solvability Theorem for Pseudo-Differential Operators""; ""Chapter III. Proof of Theorem 1""; ""3.1 General Existence Theorem for Feller Semigroups""; ""3.2 Proof of Theorem 1""; ""Chapter IV. Proof of Theorem 2""

""4.1 The Space C[sub(0)](D\M)""""4.2 Proof of Theorem 2""; ""Appendix. The Maximum Principle""; ""References""

Notes:

"September 1992, Volume 99, Number 475 (second of 4 numbers)."

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-0901-1