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On the dependence of the hitting probability of a sum of random vectors in a convex domain on its form. (Russian) Zbl 0613.60017

Some estimates of the concentration function \[ Q(S_ n,A)=\sup_{x\in {\mathbb{R}}^ s}P\{S_ n\in A+x\} \] are presented without proof. Here \(S_ n=\sum^{n}_{i=1}X_ i\), \(X_ i\), \(i\geq 1\), are independent s- dimensional random vectors. The estimates are expressed by means of so- called mean diameter Minkowski measures \(W_ i(A)\), \(0\leq i\leq s\). The same quantities \(W_ i(A)\) are used in the estimate of the remainder term in the central limit theorem and this leads to a strengthening of a result of B. von Bahr [Ark. Mat. 7, 89-99 (1967; Zbl 0221.60015).
Reviewer: V.Paulauskas

MSC:

60F05 Central limit and other weak theorems

Citations:

Zbl 0221.60015
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