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Sibirskii Matematicheskii Zhurnal, 2020, Volume 61, Number 1, Pages 29–59
DOI: https://doi.org/10.33048/smzh.2020.61.103 (Mi smj5963) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Boundary crossing problems for compound renewal processes

A. A. Borovkov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
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DOI: https://doi.org/10.33048/smzh.2020.61.103
Abstract: We find sharp asymptotics of the probability that the trajectory of a compound renewal process crosses (or does not cross) an arbitrary remote boundary. In particular, some limit theorems are obtained for the distribution of the maximum of the process in the domain of large deviations. We also give some applications to the classical ruin probability problem in insurance theory.
Keywords: compound renewal process, boundary crossing problems, large deviation, ruin probability problem.
Funding agency Grant number
Siberian Branch of Russian Academy of Sciences I.1.3 (проект № 0314-2016-0008)
Russian Foundation for Basic Research 18-01-00101_а
The author was partially supported by the Program of Basic Scientific Research of the Siberian Branch of the Russian Academy of Sciences (Grant No. I.1.3, Project 0314—2016—0008) as well as funded by the Russian Foundation for Basic Research (Grant 18—01—00101a).
Received: 27.08.2019
Revised: 26.09.2019
Accepted: 18.10.2019
English version:
Siberian Mathematical Journal, 2020, Volume 61, Issue 1, Pages 21–46
DOI: https://doi.org/10.1134/S0037446620010036
Bibliographic databases:
Document Type: Article
UDC: 519.21
MSC: 35R30
Language: Russian
Citation: A. A. Borovkov, “Boundary crossing problems for compound renewal processes”, Sibirsk. Mat. Zh., 61:1 (2020), 29–59; Siberian Math. J., 61:1 (2020), 21–46
Citation in format AMSBIB
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\by A.~A.~Borovkov
\paper Boundary crossing problems for~compound renewal processes
\jour Sibirsk. Mat. Zh.
\yr 2020
\vol 61
\issue 1
\pages 29--59
\mathnet{http://mi.mathnet.ru/smj5963}
\crossref{https://doi.org/10.33048/smzh.2020.61.103}
\transl
\jour Siberian Math. J.
\yr 2020
\vol 61
\issue 1
\pages 21--46
\crossref{https://doi.org/10.1134/S0037446620010036}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000516567300003}
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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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