V. M. Zolotarev, V. M. Kruglov, “The structure of infinitely divisible distributions on a bicompact Abelian group”, Teor. Veroyatnost. i Primenen., 20:4 (1975), 712–724; Theory Probab. Appl., 20:4 (1976), 698

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Teoriya Veroyatnostei i ee Primeneniya, 1975, Volume 20, Issue 4, Pages 712–724 (Mi tvp3336)

This article is cited in 8 scientific papers (total in 8 papers)

The structure of infinitely divisible distributions on a bicompact Abelian group

V. M. Zolotarev^a, V. M. Kruglov^b

^a V. A. Steklov Mathematical Institute, USSR Academy of Sciences
^b M. V. Lomonosov Moscow State University

Full-text PDF (838 kB) Citations (8)

Abstract: Any probability distribution can be written in the form

$F=\alpha_1F_1+\alpha_2F_2+\alpha_3F_3,\quad\alpha_j\ge0,\quad\alpha_1+\alpha_2+\alpha_3=1,$
where

$F_1$ is an absolutely continuous,

$F_2$ a singular and

$F_3$ a discrete probability distribution.
We consider the following problem: what properties of the spectral measure of an infinitely divisible distribution

$F$ involve

$\alpha_j>0$ (

$j=1,2,3$ )?

Received: 18.08.1971
Revised: 27.05.1975

English version:
Theory of Probability and its Applications, 1976, Volume 20, Issue 4, Pages 698–709
DOI: https://doi.org/10.1137/1120079

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: V. M. Zolotarev, V. M. Kruglov, “The structure of infinitely divisible distributions on a bicompact Abelian group”, Teor. Veroyatnost. i Primenen., 20:4 (1975), 712–724; Theory Probab. Appl., 20:4 (1976), 698–709

Citation in format AMSBIB

\Bibitem{ZolKru75}

\by V.~M.~Zolotarev, V.~M.~Kruglov

\paper The structure of infinitely divisible distributions on a~bicompact Abelian group

\jour Teor. Veroyatnost. i Primenen.

\yr 1975

\vol 20

\issue 4

\pages 712--724

\mathnet{http://mi.mathnet.ru/tvp3336}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=397822}

\zmath{https://zbmath.org/?q=an:0358.60027}

\transl

\jour Theory Probab. Appl.

\yr 1976

\vol 20

\issue 4

\pages 698--709

\crossref{https://doi.org/10.1137/1120079}

Linking options:

https://www.mathnet.ru/eng/tvp3336

https://www.mathnet.ru/eng/tvp/v20/i4/p712

This publication is cited in the following 8 articles:

Arnold Janssen, Thorsten Pauls, “How do bootstrap and permutation tests work?”, Ann. Statist., 31:3 (2003)
G. M. Fel'dman, “Generalized Poisson distribution on groups”, Theory Probab. Appl., 29:2 (1985), 218–230
G. M. Feldman, “Generalized Poisson distribution on groups”, Funct. Anal. Appl., 17:1 (1983), 72–74
G. M. Fel'dman, “On a decomposition of the Poisson distribution on groups”, Theory Probab. Appl., 27:4 (1983), 780–794
Arnold Janssen, “Charakterisierung stetiger Faltungshalbgruppen durch das L�vy-Ma�”, Math. Ann., 246:3 (1980), 233
Arnold Janssen, “A general purity law for convolution semigroups with discrete Lévy measure”, Semigroup Forum, 20:1 (1980), 55
G. M. Fel'dman, “On Gaussian distributions on locally compact Abelian groups”, Theory Probab. Appl., 23:2 (1979), 529–542
G. M. Feldman, “Gaussian distributions on locally compact Abelian groups”, Funct. Anal. Appl., 11:1 (1977), 76–78

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Theory of Probability and its Applications

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