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Sibirsk. Mat. Zh., 2015, Volume 56, Number 5, Pages 961–981 (Mi smj2691)  

This article is cited in 1 scientific paper (total in 1 paper)

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

A. A. Borovkovab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia

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.

Keywords: compound renewal process, first passage time through an arbitrary boundary, law of the iterated logarithm, analog of the law of the iterated logarithm in the case of infinite variance.

DOI: https://doi.org/10.17377/smzh.2015.56.501

Full text: PDF file (351 kB)
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English version:
Siberian Mathematical Journal, 2015, 56:5, 765–782

Bibliographic databases:

UDC: 519.21
Received: 01.06.2015

Citation: A. A. Borovkov, “Integral theorems for the first passage time of an arbitrary boundary by a compound renewal process”, Sibirsk. Mat. Zh., 56:5 (2015), 961–981; Siberian Math. J., 56:5 (2015), 765–782

Citation in format AMSBIB
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\paper Integral theorems for the first passage time of an arbitrary boundary by a~compound renewal process
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\yr 2015
\vol 56
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\pages 961--981
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\jour Siberian Math. J.
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\vol 56
\issue 5
\pages 765--782
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. A. Borovkov, “Integro-local limit theorems for compound renewal processes”, Theory Probab. Appl., 62:2 (2018), 175–195  mathnet  crossref  crossref  mathscinet  isi  elib
  • Сибирский математический журнал Siberian Mathematical Journal
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