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Integral theorems for the first passage time of an arbitrary boundary by a compound renewal process

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Abstract

We obtain the integral limit theorems for the first passage time through an arbitrary remote boundary by a compound renewal process both for the cases of finite and infinite variance of the process. In the latter case, we assume that some distributions belong to the attraction domain of the stable law.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    A. A. Borovkov

  2. Novosibirsk State University, Novosibirsk, Russia

    A. A. Borovkov

Authors
  1. A. A. Borovkov
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Correspondence to A. A. Borovkov.

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Original Russian Text Copyright © 2015 Borovkov A.A.

Novosibirsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 56, No. 5, pp. 961–981, September–October, 2015; DOI: 10.17377/smzh.2015.56.501.

The author was partially supported by the Russian Foundation for Basic Research (Grant 14–01–00220).

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Borovkov, A.A. Integral theorems for the first passage time of an arbitrary boundary by a compound renewal process. Sib Math J 56, 765–782 (2015). https://doi.org/10.1134/S0037446615050018

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  • DOI: https://doi.org/10.1134/S0037446615050018

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