Functional Analysis for Probability and Stochastic Processes
Functional Analysis for Probability and Stochastic Processes
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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.
- Numerous standard and non-standard examples and exercises make the book suitable for both a textbook for a course as well as for self-study
- Unique in content, range, structure and presentation
- Very detailed clear and careful proofs
Reviews & endorsements
"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
Product details
October 2005Adobe eBook Reader
9780511128219
0 pages
0kg
250 exercises
This ISBN is for an eBook version which is distributed on our behalf by a third party.
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.
