Characterization of probability distributions on locally compact Abelian 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...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2023]
|
| Schriftenreihe: | Mathematical surveys and monographs
volume 273 |
| Schlagworte: |
Probability theory and stochastic processes
> Probability theory on algebraic and topological structures
> Probability measures on groups or semigroups, Fourier transforms, factorization
Abstract harmonic analysis
> Abstract harmonic analysis
> Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups
|
| Zusammenfassung: | 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. |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | ix, 240 Seiten |
| ISBN: | 9781470472955 |
Internformat
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| 245 | 1 | 0 | |a Characterization of probability distributions on locally compact Abelian groups |c Gennadiy Feldman |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [2023] | |
| 264 | 4 | |c © 2023 | |
| 300 | |a ix, 240 Seiten | ||
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| 490 | 1 | |a Mathematical surveys and monographs |v volume 273 | |
| 500 | |a Includes bibliographical references and index | ||
| 505 | 8 | |a 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. | |
| 520 | |a 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. | ||
| 650 | 4 | |a Locally compact Abelian groups | |
| 650 | 4 | |a Distribution (Probability theory) | |
| 653 | 0 | |a Probability theory and stochastic processes -- Probability theory on algebraic and topological structures -- Probability measures on groups or semigroups, Fourier transforms, factorization | |
| 653 | 0 | |a Statistics -- Distribution theory -- Characterization and structure theory | |
| 653 | 0 | |a Abstract harmonic analysis -- Abstract harmonic analysis -- Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups | |
| 653 | 0 | |a Abstract harmonic analysis -- Abstract harmonic analysis -- Positive definite functions on groups, semigroups, etc | |
| 653 | 0 | |a Difference and functional equations -- Functional equations and inequalities -- Equations for functions with more general domains and/or ranges | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe, ebook |z 9781470473266 |
| 830 | 0 | |a Mathematical surveys and monographs |v volume 273 |w (DE-604)BV000018014 |9 273 | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-034623721 | |
Datensatz im Suchindex
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| author | Felʹdman, G. M. |
| author_GND | (DE-588)140359257 |
| author_facet | Felʹdman, G. M. |
| author_role | aut |
| author_sort | Felʹdman, G. M. |
| author_variant | g m f gm gmf |
| building | Verbundindex |
| bvnumber | BV049363605 |
| classification_rvk | SK 800 |
| contents | 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. |
| ctrlnum | (OCoLC)1380823357 (DE-599)KXP1847112978 |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| id | DE-604.BV049363605 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T22:52:42Z |
| indexdate | 2024-10-15T14:01:50Z |
| institution | BVB |
| isbn | 9781470472955 |
| language | English |
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| physical | ix, 240 Seiten |
| publishDate | 2023 |
| publishDateSearch | 2023 |
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| publisher | American Mathematical Society |
| record_format | marc |
| series | Mathematical surveys and monographs |
| series2 | Mathematical surveys and monographs |
| spelling | Felʹdman, G. M. Verfasser (DE-588)140359257 aut Characterization of probability distributions on locally compact Abelian groups Gennadiy Feldman Providence, Rhode Island American Mathematical Society [2023] © 2023 ix, 240 Seiten txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs volume 273 Includes bibliographical references and index 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. 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. Locally compact Abelian groups Distribution (Probability theory) Probability theory and stochastic processes -- Probability theory on algebraic and topological structures -- Probability measures on groups or semigroups, Fourier transforms, factorization Statistics -- Distribution theory -- Characterization and structure theory Abstract harmonic analysis -- Abstract harmonic analysis -- Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups Abstract harmonic analysis -- Abstract harmonic analysis -- Positive definite functions on groups, semigroups, etc Difference and functional equations -- Functional equations and inequalities -- Equations for functions with more general domains and/or ranges Erscheint auch als Online-Ausgabe, ebook 9781470473266 Mathematical surveys and monographs volume 273 (DE-604)BV000018014 273 |
| spellingShingle | Felʹdman, G. M. Characterization of probability distributions on locally compact Abelian groups Mathematical surveys and monographs 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. Locally compact Abelian groups Distribution (Probability theory) |
| title | Characterization of probability distributions on locally compact Abelian groups |
| title_auth | Characterization of probability distributions on locally compact Abelian groups |
| title_exact_search | Characterization of probability distributions on locally compact Abelian groups |
| title_exact_search_txtP | Characterization of probability distributions on locally compact Abelian groups |
| title_full | Characterization of probability distributions on locally compact Abelian groups Gennadiy Feldman |
| title_fullStr | Characterization of probability distributions on locally compact Abelian groups Gennadiy Feldman |
| title_full_unstemmed | Characterization of probability distributions on locally compact Abelian groups Gennadiy Feldman |
| title_short | Characterization of probability distributions on locally compact Abelian groups |
| title_sort | characterization of probability distributions on locally compact abelian groups |
| topic | Locally compact Abelian groups Distribution (Probability theory) |
| topic_facet | Locally compact Abelian groups Distribution (Probability theory) |
| volume_link | (DE-604)BV000018014 |
| work_keys_str_mv | AT felʹdmangm characterizationofprobabilitydistributionsonlocallycompactabeliangroups |