Structural aspects in the theory of probability

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Bibliographic Information

Structural aspects in the theory of probability

Herbert Heyer

(Series on multivariate analysis, v. 8)

World Scientific, c2010

2nd enl. ed. / with an additional chapter by Gyula Pap

  • : hard

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Note

Includes bibliographical references (p. 389-395) and index

Description and Table of Contents

Description

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.

Table of Contents

  • Probability Measures on Metric Spaces
  • The Fourier Transform in a Banach Space
  • The Structure of Infinitely Divisible Probability Measures
  • Harmonic Analysis of Convolution Semigroups
  • Negative Definite Functions and Convolution Semigroups
  • Probabilistic Properties of Convolution Semigroups
  • Hypergroups in Probability Theory
  • Limit Theorems on Locally Compact Abelian Groups.

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