Functional analysis for probability and stochastic processes : an introduction

A. Bobrowski

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.

「Nielsen BookData」より

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.

「Nielsen BookData」より

[目次]

  • 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 Levy processes
  • 8. Markov processes and semigroups of operators
  • 9. Appendixes
  • References
  • Index.

「Nielsen BookData」より

[目次]

  • 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 Levy processes
  • 8. Markov processes and semigroups of operators
  • 9. Appendixes
  • References
  • Index.

「Nielsen BookData」より

この本の情報

書名 Functional analysis for probability and stochastic processes : an introduction
著作者等 Bobrowski, A.
Bobrowski Adam
書名別名 Functional analysis for probability and stochastic processes
出版元 Cambridge University Press
刊行年月 2007
版表示 [Repr. with corr.]
ページ数 xii, 393 p.
大きさ 23 cm
ISBN 9780521539371
9780521831666
NCID BA91410665
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言語 英語
出版国 イギリス
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