This article is cited in 8 papers

Properties of the deviation rate function and the asymptotics for the Laplace thansform of the distribution of a compound renewal process

A. A. Borovkov, A. A. Mogul'skii, E. I. Prokopenko

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: We find the asymptotics for the logarithm of the Laplace transform of the distribution of a compound renewal process as time increases unboundedly. It is assumed that the elements of the governing sequences of the renewal process satisfy Cramér's moment condition. Representations for the deviation rate function of the compound renewal process are found.

Keywords: compound renewal process, large deviations, large deviation principle, Cramér's condition, deviation rate function, Legendre transform, Laplace transform asymptotics.

Received: 26.12.2018
Accepted: 12.02.2019

DOI: 10.4213/tvp5285

 English version: Theory of Probability and its Applications, 2020, 64:4, 499–512

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