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 Teor. Veroyatnost. i Primenen.: Year: Volume: Issue: Page: Find

 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:

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}