Structural Aspects in the Theory of Probability: A Primer in Probabilities on Algebraic: Topological Structures

Structural Aspects in the Theory of Probability: A Primer in Probabilities on Algebraic: Topological Structures

by Herbert Heyer
     
 

ISBN-10: 9812389377

ISBN-13: 9789812389374

Pub. Date: 08/01/2004

Publisher: World Scientific Publishing Company, Incorporated

This book focuses on the algebraic-topological aspects of probability theory, 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. The method applied within the setting of Banach spaces and of locally compact Abelian groups is that…  See more details below

Overview

This book focuses on the algebraic-topological aspects of probability theory, 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. The method applied within the setting of Banach spaces and of locally compact Abelian groups is that of the Fourier transform. This analytic tool along with the relevant parts of harmonic analysis makes it possible to study certain properties of stochastic processes in dependence of the algebraic-topological structure of their state spaces. Graduate students, lecturers and researchers may use the book as a primer in the theory of probability measures on groups and related structures.This book has been selected for coverage in:• CC / Physical, Chemical & Earth Sciences• Index to Scientific Book Contents® (ISBC)

Product Details

ISBN-13:
9789812389374
Publisher:
World Scientific Publishing Company, Incorporated
Publication date:
08/01/2004
Series:
Series on Multivariate Analysis, #7
Pages:
388
Product dimensions:
6.30(w) x 8.90(h) x 1.10(d)

Table of Contents

1Probability measures on metric spaces
2The Fourier transform in a Banach space
3The structure of infinitely divisible probability measures
4Harmonic analysis of convolution semigroups
5Negative definite functions and convolution semigroups
6Probabilistic properties of convolution semigroups
App. ATopological groups
App. BTopological vector spaces
App. CCommutative Banach algebras

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