Functional Analysis for Probability and Stochastic Processes: An Introduction

by Adam Bobrowski

Overview

Designed for students of probability and stochastic processes, as well as for students of functional analysis, specifically, this volume presents some chosen parts of functional analysis that can help clarify probability and stochastic processes. The subjects range from basic Hilbert and Banach spaces, through weak topologies and Banach algebras, to the theory of semigroups of bounded linear operators. Numerous standard and non-standard examples and exercises make the book suitable as a course textbook or for self-study.

Product Details

ISBN-13:	9780521831666
Publisher:	Cambridge University Press
Publication date:	08/11/2005
Pages:	408
Product dimensions:	6.22(w) x 9.29(h) x 1.10(d)

About the Author

Adam Bobrowski is a Professor of Mathematics at Lublin University.

Table of Contents

Preface; 1. Preliminaries, notations and conventions; 2. Basic notions in functional analysis; 3. Conditional expectation; 4. Brownian motion and Hilbert spaces; 5. Dual spaces and convergence of probability measures; 6. The Gelfand transform and its applications; 7. Semigroups of operators and Lévy processes; 8. Markov processes and semigroups of operators; 9. Appendixes; References; Index.

Editorial Reviews

"My impression is that this text might well succeed as an attractive introduction to, or even as propaganda for the subject of probability and stochastic processes for a well-educated analyst without a probabilistic background."
N.H. Bingham, Journal of the American Statistical Association

From the Publisher