WIAS Preprint No. 1036, (2005)

Exponential bounds for the probability deviations of sums of random fields


  • Kurbanmuradov, Orazgeldy
  • Sabelfeld, Karl

2010 Mathematics Subject Classification

  • 65C05 60F10 65C50


  • Moderately large deviations, Bernstein's inequality, sums of random fields, deviation probability, optimal asymptotics, sample continuity modulus




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.

Appeared in

  • Monte Carlo Methods Appl., 12 (2006) pp. 211--229.

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