Functional Analysis for Probability and Stochastic Processes: An Introduction

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Cambridge University Press, Aug 11, 2005 - Mathematics - 393 pages
This text is designed both for students of probability and stochastic processes, and for students of functional analysis. 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 as well as for self-study.
 

Contents

4
23
5
29
Basic notions in functional analysis
37
3
63
23
70
5548
76
4
115
Brownian motion and Hilbert spaces
121
2
127
Dual spaces and convergence of probability measures
147
The Gelfand transform and its applications
201
Semigroups of operators and Lévy processes
234
Markov processes and semigroups of operators
294
Appendixes
363
References
385
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About the author (2005)

Adam Bobrowski is a Professor of Mathematics at Lublin University.

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