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Arithmetic of probability distributions, and characterization problems on Abelian groups

Author: G M Felʹdman; Simeon Ivanov
Publisher: Providence, R.I. : American Mathematical Society, ©1993.
Series: Translations of mathematical monographs, v. 116.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
This book studies the problem of the decomposition of a given random variable into a sum of independent random variables (components). Starting from the famous Cramér theorem, which says that all components of a normal random variable are also normal random variables, the central feature of the book is Fel‴dman's use of powerful analytical techniques. In the algebraic case, one cannot directly use analytic methods  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Felʹdman, G. M. (Gennadĭ Mikaĭlovich).
Arithmetic of probability distributions, and characterization problems on Abelian groups.
Providence, R.I. : American Mathematical Society, ©1993
(DLC) 92045025
(OCoLC)27171968
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: G M Felʹdman; Simeon Ivanov
ISBN: 9781470445270 1470445271
OCLC Number: 1031955781
Description: 1 online resource.
Contents: Introduction Chapter I. Auxiliary results Chapter II. Arithmetic of distributions Chapter III. Characterization problems
Series Title: Translations of mathematical monographs, v. 116.
Other Titles: Arifmetika veroi︠a︡tnostnykh raspredeleniĭ i kharakterizat︠s︡ionnye zadachi na abelevykh gruppakh.
Responsibility: G.M. Feldman ; [translated from the Russian by Yu. Lyiubarskii ; translation edited by Simeon Ivanov].

Abstract:

This book studies the problem of the decomposition of a given random variable into a sum of independent random variables (components). Starting from the famous Cramér theorem, which says that all components of a normal random variable are also normal random variables, the central feature of the book is Fel‴dman's use of powerful analytical techniques. In the algebraic case, one cannot directly use analytic methods because of the absence of a natural analytic structure on the dual group, which is the domain of characteristic functions. Nevertheless, the methods developed in this book allow one.

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