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On large deviations for Poisson stochastic integrals

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Abstract

We obtain asymptotically exact estimates for large deviations of Poisson stochastic integrals. We also find a region where such an integral can be approximated by the corresponding Gaussian random variable. In of all these results, we obtain nonasymptotic estimates for remainder terms.

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Authors and Affiliations

  1. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia

    M. V. Burnashev

  2. Laboratoire Manceau de Mathématiques, Université du Maine, Le Mans, France

    Yu. A. Kutoyants

Authors
  1. M. V. Burnashev
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  2. Yu. A. Kutoyants
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Correspondence to M. V. Burnashev.

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Original Russian Text © M.V. Burnashev, Yu.A. Kutoyants, 2012, published in Problemy Peredachi Informatsii, 2012, Vol. 48, No. 1, pp. 64–79.

Supported in part by the Russian Foundation for Basic Research, project no. 09-01-00536.

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Burnashev, M.V., Kutoyants, Y.A. On large deviations for Poisson stochastic integrals. Probl Inf Transm 48, 56–69 (2012). https://doi.org/10.1134/S0032946012010061

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  • DOI: https://doi.org/10.1134/S0032946012010061

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