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A Local Large Deviation Principle for Inhomogeneous Birth–Death Processes

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Abstract

The paper considers a continuous-time birth–death process where the jump rate has an asymptotically polynomial dependence on the process position. We obtain a rough exponential asymptotic for the probability of trajectories of a re-scaled process contained within a neighborhood of a given continuous nonnegative function.

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Author information

Authors and Affiliations

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

    N. D. Vvedenskaya & Yu. M. Suhov

  2. Laboratory of Applied Mathematics, Novosibirsk State University, Novosibirsk, Russia

    A. V. Logachov

  3. Laboratory of Probability Theory and Mathematical Statistics, Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

    A. V. Logachov

  4. Statistics Division, Novosibirsk State University of Economics and Management, Novosibirsk, Russia

    A. V. Logachov

  5. Mathematical Department, Pennsylvania State University, University Park, State College, PA, USA

    Yu. M. Suhov

  6. Department of Statistics, Institute of Mathematics and Statistics, University of São Paulo, São Paulo, Brazil

    A. A. Yambartsev

Authors
  1. N. D. Vvedenskaya
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  2. A. V. Logachov
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  3. Yu. M. Suhov
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  4. A. A. Yambartsev
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Corresponding author

Correspondence to N. D. Vvedenskaya.

Additional information

Original Russian Text © N.D. Vvedenskaya, A.V. Logachov, Yu.M. Suhov, A.A. Yambartsev, 2018, published in Problemy Peredachi Informatsii, 2018, Vol. 54, No. 3, pp. 73–91.

The research was carried out at the Institute for Information Transmission Problems of the Russian Academy of Sciences at the expense of the Russian Science Foundation, project no. 14-50-00150.

The research was carried out at the expense of the Russian Science Foundation, project no. 18-11-00129.

Supported by the Brazilian National Council for Scientific and Technological Development (CNPq), grant no. 301050/2016-3, and São Paulo Research Foundation (FAPESP), grant no. 2017/10555-0.

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Vvedenskaya, N.D., Logachov, A.V., Suhov, Y.M. et al. A Local Large Deviation Principle for Inhomogeneous Birth–Death Processes. Probl Inf Transm 54, 263–280 (2018). https://doi.org/10.1134/S0032946018030067

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  • DOI: https://doi.org/10.1134/S0032946018030067

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