Characterization of Probability Distributions on Locally Compact Abelian Groups
Seiten
2023
American Mathematical Society (Verlag)
978-1-4704-7295-5 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-7295-5 (ISBN)
Provides 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.
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.
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.
Gennadiy Feldman, B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences, Kharkiv, Ukraine.
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
| Erscheinungsdatum | 11.07.2023 |
|---|---|
| Reihe/Serie | Mathematical Surveys and Monographs |
| Verlagsort | Providence |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Gewicht | 205 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik | |
| ISBN-10 | 1-4704-7295-3 / 1470472953 |
| ISBN-13 | 978-1-4704-7295-5 / 9781470472955 |
| Zustand | Neuware |
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Buch | Hardcover (2022)
Hanser, Carl (Verlag)
CHF 41,95
