Ebook: Probability Measures on Locally Compact Groups
Author: Herbert Heyer (auth.)
- Tags: Mathematics general
- Series: Ergebnisse der Mathematik und ihrer Grenzgebiete 94
- Year: 1977
- Publisher: Springer-Verlag Berlin Heidelberg
- Edition: 1
- Language: English
- pdf
Probability measures on algebraic-topological structures such as topological semi groups, groups, and vector spaces have become of increasing importance in recent years for probabilists interested in the structural aspects of the theory as well as for analysts aiming at applications within the scope of probability theory. In order to obtain a natural framework for a first systematic presentation of the most developed part of the work done in the field we restrict ourselves to prob ability measures on locally compact groups. At the same time we stress the non Abelian aspect. Thus the book is concerned with a set of problems which can be regarded either from the probabilistic or from the harmonic-analytic point of view. In fact, it seems to be the synthesis of these two viewpoints, the initial inspiration coming from probability and the refined techniques from harmonic analysis which made this newly established subject so fascinating. The goal of the presentation is to give a fairly complete treatment of the central limit problem for probability measures on a locally compact group. In analogy to the classical theory the discussion is centered around the infinitely divisible probability measures on the group and their relationship to the convergence of infinitesimal triangular systems.
Content:
Front Matter....Pages I-X
Introduction....Pages 1-4
Preliminaries....Pages 5-16
Harmonic Analysis of Almost Periodic Locally Compact Groups....Pages 17-86
Convergence of Convolution Sequences of Probability Measures....Pages 87-162
Embedding of Infinitely Divisible Probability Measures....Pages 163-248
Canonical Representations of Convolution Semigroups....Pages 249-335
The Central Limit Problem in the Abelian Case....Pages 336-407
The Central Limit Problem in the General Case....Pages 408-503
Back Matter....Pages 504-534
Content:
Front Matter....Pages I-X
Introduction....Pages 1-4
Preliminaries....Pages 5-16
Harmonic Analysis of Almost Periodic Locally Compact Groups....Pages 17-86
Convergence of Convolution Sequences of Probability Measures....Pages 87-162
Embedding of Infinitely Divisible Probability Measures....Pages 163-248
Canonical Representations of Convolution Semigroups....Pages 249-335
The Central Limit Problem in the Abelian Case....Pages 336-407
The Central Limit Problem in the General Case....Pages 408-503
Back Matter....Pages 504-534
....