Structural Aspects in the Theory of Probability (2nd Enlarged Edition) / Edition 2

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Overview

The book is conceived as a text accompanying the traditional graduate courses on probability theory. An important feature of this enlarged version is the emphasis on algebraic-topological aspects leading to a wider and deeper understanding of basic theorems such as those on the structure of continuous convolution semigroups and the corresponding processes with independent increments. Fourier transformation-the method applied within the settings of Banach spaces, locally compact Abelian groups and commutative hypergroups-is given an in-depth discussion. This powerful analytic tool along with the relevant facts of harmonic analysis make it possible to study certain properties of stochastic processes in dependence of the algebraic-topological structure of their state spaces. In extension of the first edition, the new edition contains chapters on the probability theory of generalized convolution structures such as polynomial and Sturm-Liouville hypergroups, and on the central limit problem for groups such as tori, p-adic groups and solenoids.

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Product Details

  • ISBN-13: 9789814282482
  • Publisher: World Scientific Publishing Company, Incorporated
  • Publication date: 9/28/2009
  • Edition description: Enlarged
  • Edition number: 2
  • Pages: 424
  • Product dimensions: 6.20 (w) x 9.00 (h) x 1.10 (d)

Table of Contents

1 Probability Measures on Metric Spaces 1

2 The Fourier Transform in a Banach Space 29

3 The Structure of Infinitely Divisible Probability Measures 71

4 Harmonic Analysis of Convolution Semigroups 133

5 Negative Definite Functions and Convolution Semigroups 185

6 Probabilistic Properties of Convolution Semigroups 225

7 Hypergroups in Probability Theory 291

8 Limit Theorems on Locally Compact Abelian Groups 345

Appendix A Topological groups 375

Appendix B Topological vector spaces 377

Appendix C Commutative Banach algebras 383

Selected References 389

Symbols 397

Index 403

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