Characterization of probability distributions on locally compact Abelian groups /

Characterization of probability distributions on locally compact Abelian groups /

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Bibliographic Details
Author / Creator:	Felʹdman, G. M. (Gennadiĭ Mikhaĭlovich), author.
Imprint:	Providence, Rhode Island : American Mathematical Society, [2023] ©2023
Description:	ix, 240 pages : illustrations ; 26 cm.
Language:	English
Series:	Mathematical surveys and monographs, 0076-5376 ; volume 273 Mathematical surveys and monographs ; no. 273.
Subject:	Locally compact Abelian groups. Distribution (Probability theory) Distribution (Probability theory) Locally compact Abelian groups.
Format:	Print Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/13125102

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Other authors / contributors:	American Mathematical Society, issuing body.
ISBN:	9781470472955 1470472953 9781470473266
Notes:	Includes bibliographical references and indexes.
Summary:	"It is well known that if two independent identically distributed random variables are Gaussian, then their sum and difference are also independent. It turns out that only Gaussian random variables have such property. This statement, known as the famous Kac-Bernstein theorem, is a typical example of a so-called characterization theorem. Characterization theorems in mathematical statistics are statements in which the description of possible distributions of random variables follows from properties of some functions of these random variables. The first results in this area are associated with famous 20th century mathematicians such as G. Pólya, M. Kac, S. N. Bernstein, and Yu. V. Linnik. By now, the corresponding theory on the real line has basically been constructed. The problem of extending the classical characterization theorems to various algebraic structures has been actively studied in recent decades. The purpose of this book is to provide a comprehensive and self-contained overview of the current state of the theory of characterization problems on locally compact Abelian groups. The book will be useful to everyone with some familiarity of abstract harmonic analysis who is interested in probability distributions and functional equations on groups" --

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Call Number:	QA387.F445 2023
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