Characterization of a class of infinitely divisible distributions in Hilbert space |
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Authors: | V M Kruglov |
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Institution: | 1. M. V. Lomonosov Moscow State University, USSR
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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 ∫ H exp (α∥x∥ In (∥x∥+1))dF is finite for some numberα>0. If this integral is finite for anyα>0 then the infinitely divisible distribution F is normal (maybe, degenerate). |
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