Functional Analysis for Probability and Stochastic Processes
An Introduction

This text is designed both for students of probability and stochastic processes, and for students of functional analysis.

Adam Bobrowski (Author)

9780521831666, Cambridge University Press

Hardback, published 11 August 2005

408 pages, 250 exercises
23.6 x 15.8 x 2.8 cm, 0.775 kg

"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

This text is designed both for students of probability and stochastic processes, and for students of functional analysis. For the reader not familiar with functional analysis a detailed introduction to necessary notions and facts is provided. However, this is not a straight textbook in functional analysis; rather, it presents some chosen parts of functional analysis that can help understand ideas from 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.

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.

Subject Areas: Probability & statistics [PBT], Functional analysis & transforms [PBKF]