Exponential bounds for the probability deviations of sums of random fields

Kurbanmuradov O. and Sabelfeld K.
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Kurbanmuradov O.: 1. Center for Phys. Math. Research, Turkmenian State University, Turkmenbashy av. 31, 744000 Ashgabad, Turkmenistan
Sabelfeld K.: 2. Weierstrass Institute for Applied Analysis and Stochastics Mohrenstrasse 39, D – 10117 Berlin, Germany sabelfel@wias-berlin.de

Monte Carlo Methods and Applications, 2006, vol. 12, issue 3, 211-229

Abstract: Non-asymptotic exponential upper bounds for the deviation probability for a sum of independent random fields are obtained under Bernstein's condition and assumptions formulated in terms of Kolmogorov's metric entropy. These estimations are constructive in the sense that all the constants involved are given explicitly. In the case of moderately large deviations, the upper bounds have optimal log-asymptotices. The exponential estimations are extended to the local and global continuity modulus for sums of independent samples of a random field. The motivation of the present study comes mainly from the dependence Monte Carlo methods.

Date: 2006
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DOI: 10.1515/156939606778705218

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