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Sibirskii Matematicheskii Zhurnal, 2015, Volume 56, Number 5, Pages 961–981
DOI: https://doi.org/10.17377/smzh.2015.56.501 (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
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DOI: https://doi.org/10.17377/smzh.2015.56.501
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.
Received: 01.06.2015
English version:
Siberian Mathematical Journal, 2015, Volume 56, Issue 5, Pages 765–782
DOI: https://doi.org/10.1134/S0037446615050018
Bibliographic databases:
Document Type: Article
UDC: 519.21
Language: Russian
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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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Сибирский математический журнал Siberian Mathematical Journal
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