確率論の構造（拡大版） Structural Aspects in the Theory of Probability (2nd Enlarged Edition) (Series on Multivariate Analysis) （2nd enlarged）

Heyer, Herbert

World Scientific Publishing Co Pte Ltd（2009/09発売）

• 製本 Hardcover:ハードカバー版／ページ数 424 p.
• 言語 ENG
• 商品コード 9789814282482
• DDC分類 519.2

基本説明

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.

Full 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.

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.