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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.Read more
- 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
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- Date Published: October 2005
- format: Adobe eBook Reader
- isbn: 9780511128219
- contains: 250 exercises
- availability: Adobe Reader ebooks available from eBooks.com
Table of Contents
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
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