|
Teoriya Veroyatnostei i ee Primeneniya, 1967, Volume 12, Issue 3, Pages 559–562
(Mi tvp739)
|
|
|
|
This article is cited in 5 scientific papers (total in 5 papers)
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 $0<n_1<n_2<\dots$ 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.
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
Linking options:
https://www.mathnet.ru/eng/tvp739 https://www.mathnet.ru/eng/tvp/v12/i3/p559
|
Statistics & downloads: |
Abstract page: | 215 | Full-text PDF : | 89 |
|