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Journal Article

Limit Theorems for Sums of Independent Random Variables with Values in a Hilbert Space

S. R. S. Varadhan
Sankhyā: The Indian Journal of Statistics, Series A (1961-2002)
Vol. 24, No. 3 (Aug., 1962), pp. 213-238
Stable URL: http://www.jstor.org/stable/25049213
Page Count: 26
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Limit Theorems for Sums of Independent Random Variables with Values in a Hilbert Space
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Abstract

In this article distributions on a Real Separable Hilbert Space are considered. Limit distributions are derived for sums of infinitesimal random variables. A representation similar to the Levy-Khintchine representation is derived for infinitely divisible distributions. Necessary and sufficient conditions for compactness are obtained in terms of the quantities occurring in the representation.

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