Characterization of probability distributions on locally compact Abelian groups

著者

• Felʹdman, G. M. (Gennadiĭ Mikhaĭlovich)

書誌事項

Characterization of probability distributions on locally compact Abelian groups

Gennadiy Feldman

（Mathematical surveys and monographs, v. 273）

American Mathematical Society, c2023

• : pbk

タイトル別名

Characterization of probability distributions on groups

注記

Includes bibliographical references (p. 231-235) and indexes

内容説明・目次

内容説明

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. Polya, 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.

目次

Preliminaries Independent random variables with independent sum and difference Characterization of probability distributions through the independence of linear forms Characterization of probability distributions through the symmetry of the conditional distribution of one linear form given another Characterization theorems on the field of $p$-adic numbers Miscellaneous characterization theorems Bibliography Index Index of symbols

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詳細情報

• NII書誌ID(NCID): BD01734333
• ISBN:
  • 9781470472955
• LCCN: 2022059184
• 出版国コード: us
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Providence, R.I.
• ページ数/冊数: ix, 240 p.
• 大きさ: 26 cm
• 分類:
  • LCC : QA387
  • DC23 : 519.2/4
• 件名:
  • LCSH : Locally compact Abelian groups
  • LCSH : Distribution (Probability theory)
• 親書誌ID:
  • BA00134419