This article is cited in 4 papers

Characterization of a class of infinitely divisible distributions in Hilbert space

V. M. Kruglov

M. V. Lomonosov Moscow State University

Abstract: It is established that the spectral measure of an infinitely divisible distribution $F$ in a Hilbert space $H$ is concentrated in a sphere of finite radius if and only if the integral $\int_H\exp(\alpha\|x\|\ln(\|x\|+1))\,dF$ is finite for some number $\alpha>0$. If this integral is finite for any $\alpha>0$ then the infinitely divisible distribution $F$ is normal (maybe, degenerate).

UDC: 519.88

Received: 21.05.1973

 English version: Mathematical Notes, 1974, 16:5, 1057–1060

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