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Asymptotic expansions of the probability that the sum of independent random variables hits a ball in a Hilbert space. (English. Russian original) Zbl 0860.60006
Russ. Math. Surv. 50, No. 5, 1045-1063 (1995); translation from Usp. Mat. Nauk 50, No. 5, 203-222 (1995).
This paper deals with estimates of the remainder and the terms of the asymptotic expansion of the probability that the sum of independent random variables hits a ball in a Hilbert space. The aim of this note is to construct non-uniform estimates with explicit dependence on the center of the ball, and with minimal moment conditions. It should be noted that the dependence of estimates on (truncated) moments and covariance operators of the terms is given explicitly.

MSC:
60B12 Limit theorems for vector-valued random variables (infinite-dimensional case)
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