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

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

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English version:
Siberian Mathematical Journal, 2015, 56:5, 765–782

Bibliographic databases:

UDC: 519.21

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
\Bibitem{Bor15} \by A.~A.~Borovkov \paper Integral theorems for the first passage time of an arbitrary boundary by a~compound renewal process \jour Sibirsk. Mat. Zh. \yr 2015 \vol 56 \issue 5 \pages 961--981 \mathnet{http://mi.mathnet.ru/smj2691} \crossref{https://doi.org/10.17377/smzh.2015.56.501} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3492884} \elib{http://elibrary.ru/item.asp?id=24817490} \transl \jour Siberian Math. J. \yr 2015 \vol 56 \issue 5 \pages 765--782 \crossref{https://doi.org/10.1134/S0037446615050018} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000363722400001} \elib{http://elibrary.ru/item.asp?id=24963030} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84944873377} 

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• http://mi.mathnet.ru/eng/smj/v56/i5/p961

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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
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