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Exponential bounds for the probability deviations of sums of random fields

Author

Listed:
  • 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)

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.

Suggested Citation

  • Kurbanmuradov O. & Sabelfeld K., 2006. "Exponential bounds for the probability deviations of sums of random fields," Monte Carlo Methods and Applications, De Gruyter, vol. 12(3), pages 211-229, October.
    • Handle: RePEc:bpj:mcmeap:v:12:y:2006:i:3:p:211-229:n:8
    DOI: 10.1515/156939606778705218
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    References listed on IDEAS

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    1. Dembo, Amir & Zajic, Tim, 1997. "Uniform large and moderate deviations for functional empirical processes," Stochastic Processes and their Applications, Elsevier, vol. 67(2), pages 195-211, May.
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    Cited by:

    1. Kozachenko Yu. V. & Mlavets Yu. Yu., 2011. "Probability of large deviations of sums of random processes from Orlicz space," Monte Carlo Methods and Applications, De Gruyter, vol. 17(2), pages 155-168, January.
    2. Kozachenko Yuriy V. & Mlavets Yuriy Y., 2015. "Reliability and accuracy in the space Lp(T) for the calculation of integrals depending on a parameter by the Monte Carlo method," Monte Carlo Methods and Applications, De Gruyter, vol. 21(3), pages 233-244, September.

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