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On probabilities of large deviations in some classes of k-dimensional Borel sets

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  • Rozovsky, L. V.

Abstract

Let X1, X2,..., be a sequence of independent identically distributed random vectors in k-dimensional Euclidean space Rk and let [Phi](A) be the standard normal distribution in Rk, Sn = X1 + ... + Xn. In this paper a behavior of a relation P{1/[radical sign]nSn [set membership, variant] A}/[Phi](A) when set A is contained in some class of Borel sets and [Phi](A) --> 0, n --> [infinity], is investigated. Particularly, the conditions are obtained which are necessary and sufficient for 40 uniformly in all sets A which are the differences between convex Borel sets in Rk satisfying the condition 62 Here [Lambda](z) is a function such that [Lambda](z) [short up arrow] [infinity], [Lambda](z)/z[var epsilon]0 [downwards arrow] 0, 0

Suggested Citation

  • Rozovsky, L. V., 1985. "On probabilities of large deviations in some classes of k-dimensional Borel sets," Journal of Multivariate Analysis, Elsevier, vol. 17(1), pages 1-26, August.
    • Handle: RePEc:eee:jmvana:v:17:y:1985:i:1:p:1-26
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