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Large Deviation Principles for the Processes Admitting Embedded Compound Renewal Processes

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Abstract

We obtain limit theorems in the domain of large and moderate deviations for the processes admitting embedded compound renewal processes. We justify the large and moderate deviation principles for the trajectories of periodic compound renewal processes with delay and find a moderate deviation principle for the trajectories of semi-Markov compound renewal processes.

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Acknowledgments

The authors are grateful to A.A. Borovkov for advice on the statement of the problem and great help in writing this paper. The authors are grateful to the referee for valuable comments.

Funding

The work is supported by the Mathematical Center in Akademgorodok under Agreement 075–15–2019–1675 with the Ministry of Science and Higher Education of the Russian Federation.

Author information

Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    A. V. Logachov & A. A. Mogulskii

  2. Novosibirsk State Technical University, Novosibirsk, Russia

    A. V. Logachov

  3. Novosibirsk State University, Novosibirsk, Russia

    A. A. Mogulskii

Authors
  1. A. V. Logachov
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  2. A. A. Mogulskii
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Corresponding author

Correspondence to A. V. Logachov.

Additional information

Translated from Sibirskii Matematicheskii Zhurnal, 2022, Vol. 63, No. 1, pp. 145–166. https://doi.org/10.33048/smzh.2022.63.110

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Logachov, A.V., Mogulskii, A.A. Large Deviation Principles for the Processes Admitting Embedded Compound Renewal Processes. Sib Math J 63, 119–137 (2022). https://doi.org/10.1134/S0037446622010104

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  • DOI: https://doi.org/10.1134/S0037446622010104

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