Arithmetic of Probability Distributions, and Characterization Problems on Abelian Groups (Translations of Mathematical Monographs) - Hardcover

G. M. Feldman

Hardcover

ISBN 10: 0821845934 ISBN 13: 9780821845936

Publisher: American Mathematical Society, 1993

Synopsis

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 Cramer theorem, which says that all components of a normal random variable are also normal random variables, the central feature of the book is Feldman'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 to apply analytic techniques in the algebraic setting. The first part of the book presents results on the arithmetic of probability distributions of random variables with values in a locally compact abelian group. The second part studies problems of characterization of a Gaussian distribution of a locally compact abelian group by the independence or identical distribution of its linear statistics.

About this title

Language Notes

Text: English (translation)
Original Language: Russian

Edition details

• Publisher: American Mathematical Society
• Publication date: 1993
• Language: English
• ISBN 10: 0821845934
• ISBN 13: 9780821845936
• Binding: Hardcover
• Number of pages: 223