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The Large Deviation Principle for Finite-Dimensional Distributions of Multidimensional Renewal Processes

Abstract

We study two types of multidimensional compound renewal processes (c.r.p.). We assume that the elements of the sequences that control the processes satisfy Cramér’s moment condition. Wide conditions are proposed under which the large deviation principle holds for finite-dimensional distributions of the processes.

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Funding

The work was supported by the Russian Science Foundation (grant no. 18-11-00129).

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Correspondence to A. A. Mogul’skiĭ or E. I. Prokopenko.

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Mogul’skiĭ, A.A., Prokopenko, E.I. The Large Deviation Principle for Finite-Dimensional Distributions of Multidimensional Renewal Processes. Sib. Adv. Math. 31, 188–208 (2021). https://doi.org/10.1134/S1055134421030032

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Keywords

  • large deviations
  • compound renewal process
  • Cramér’s condition
  • deviation rate function
  • basic function
  • Laplace transform