Short Communications

Exponential bounds for smooth fields

V. V. Yurinskii

Moscow

Abstract: Theorem of Section 3 gives exponentially decreasing bounds on sup norm large deviation probabilities for sums of independent random fields over the $k$-dimensional unit cube. Summands are supposed to have sufficiently smooth sample functions (4), (7) and satisfy Cramer's type conditions (5), (6). Proofs are based on Sobolev's imbedding theorems.

Received: 16.11.1972

 English version: Theory of Probability and its Applications, 1974, 19:1, 221–226

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