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Teoriya Veroyatnostei i ee Primeneniya, 1958, Volume 3, Issue 2, Pages 197–200
(Mi tvp4930)
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This article is cited in 12 scientific papers (total in 12 papers)
Short Communications
Distribution of the Superposition of Infinitely Divisible Processes
V. M. Zolotarev Moscow
Abstract:
In this paper it is proved that for an arbitrary infinitely divisible process $\xi (t)$ and any non-negative infinitely divisible process $\eta(t)$ the distribution of their superposition $\xi(t)=\xi[\eta(t)]$ is also infinitely divisible. The corresponding spectral function $H(x)$ of that process (Levy function) is constructed. The second result is as follows: If in the sum $\zeta(t)=\xi_1+\cdots+\xi_{\eta(t)}$ all random variables are independent, process $\eta(t)$ has an infinitely divisible distribution, and the random variable $\xi_i$ satisfies condition $(V)$, then the distribution $\zeta(t)$ is infinitely divisible.
Received: 25.03.1958
Citation:
V. M. Zolotarev, “Distribution of the Superposition of Infinitely Divisible Processes”, Teor. Veroyatnost. i Primenen., 3:2 (1958), 197–200; Theory Probab. Appl., 3:2 (1958), 185–188
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Abstract page: | 161 | Full-text PDF : | 88 |
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