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Characterization of Probability Distributions on Locally Compact Abelian Groups
 
Gennadiy Feldman B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences, Kharkiv, Ukraine
Softcover ISBN:  978-1-4704-7295-5
Product Code:  SURV/273
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-1-4704-7326-6
Product Code:  SURV/273.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-1-4704-7295-5
eBook: ISBN:  978-1-4704-7326-6
Product Code:  SURV/273.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
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Characterization of Probability Distributions on Locally Compact Abelian Groups
Gennadiy Feldman B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences, Kharkiv, Ukraine
Softcover ISBN:  978-1-4704-7295-5
Product Code:  SURV/273
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-1-4704-7326-6
Product Code:  SURV/273.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-1-4704-7295-5
eBook ISBN:  978-1-4704-7326-6
Product Code:  SURV/273.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
  • Book Details
     
     
    Mathematical Surveys and Monographs
    Volume: 2732023; 240 pp
    MSC: Primary 60; 62; 43; Secondary 39

    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.

    Readership

    Graduate students and researchers interested in probability distributions or functional equations on groups.

  • Table of Contents
     
     
    • Chapters
    • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 2732023; 240 pp
MSC: Primary 60; 62; 43; Secondary 39

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.

Readership

Graduate students and researchers interested in probability distributions or functional equations on groups.

  • Chapters
  • 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
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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