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Teor. Veroyatnost. i Primenen., 1967, Volume 12, Issue 3, Pages 559–562 (Mi tvp739)  

Short Communications

On $M$-divisibility of stable laws of stable laws

V. M. Zolotarev

Moscow

Abstract: A one dimensional distribution $F$ is called $M$-infinitely divisible ($M$-i. d.) if there exists a sequence of integers $0<n_1<n_2<…$ such that for every $n_j$ it equal to the distribution of the product of some $n_j$ independent identically distributed random variables.
It is shown that the stable laws with parameters ($\alpha<1$, $\gamma=0$), ($\alpha=1$, $\beta=0$), ($\alpha>1$, $\gamma=0$, $\beta=0$) are $M$-i. d. but the stable laws with parameters ($\alpha>1$, $\gamma=0$, $\beta\ne0$) are not $M$-i. d.

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English version:
Theory of Probability and its Applications, 1967, 12:3, 506–508

Bibliographic databases:

Received: 24.01.1967

Citation: V. M. Zolotarev, “On $M$-divisibility of stable laws of stable laws”, Teor. Veroyatnost. i Primenen., 12:3 (1967), 559–562; Theory Probab. Appl., 12:3 (1967), 506–508

Citation in format AMSBIB
\Bibitem{Zol67}
\by V.~M.~Zolotarev
\paper On $M$-divisibility of stable laws of stable laws
\jour Teor. Veroyatnost. i Primenen.
\yr 1967
\vol 12
\issue 3
\pages 559--562
\mathnet{http://mi.mathnet.ru/tvp739}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=220334}
\zmath{https://zbmath.org/?q=an:0178.21301}
\transl
\jour Theory Probab. Appl.
\yr 1967
\vol 12
\issue 3
\pages 506--508
\crossref{https://doi.org/10.1137/1112062}


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