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Asymptotics of the Distribution Tail of the Sojourn Time for a Random Walk in a Domain of Moderate Large Deviations

Abstract

An asymptotics is obtained for the distribution tail of the sojourn time for a homogeneous random walk defined on \([0,n]\), above a receding level in a domain of moderate large deviations under Cramér’s condition on the jump distribution.

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Funding

This work was supported by the Russian Foundation for Basic Research (project No. 18–01–00074 and 19-31-90038) and by the state contract of the Sobolev Institute of Mathematics No. I.1.3 (project No. 0314-2020-0008).

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Correspondence to I. S. Borisov or E. I. Shefer.

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Borisov, I.S., Shefer, E.I. Asymptotics of the Distribution Tail of the Sojourn Time for a Random Walk in a Domain of Moderate Large Deviations. Sib. Adv. Math. 30, 162–176 (2020). https://doi.org/10.3103/S1055134420030025

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Keywords

  • random walk
  • Cramér’s condition
  • sojourn time
  • moderate large deviations