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Sibirskii Matematicheskii Zhurnal, 2019, Volume 60, Number 6, Pages 1229–1246
DOI: https://doi.org/10.33048/smzh.2019.60.604 (Mi smj3145) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Integro-local theorems in boundary crossing problems for compound renewal processes

A. A. Borovkov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
Full-text PDF (473 kB) Citations (1)
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DOI: https://doi.org/10.33048/smzh.2019.60.604
Abstract: We find sharp asymptotics for the probability that the moment when the trajectory of a compound renewal process crosses an arbitrary remote boundary lies in a prescribed small time interval. As a key step in our proof, we obtain limit theorems for the conditional distribution of jumps of the process when the endpoint of the trajectory of a compound renewal process is fixed.
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 (Program No. I.1.3, Project 0314-2016-0008) and 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, 2019, Volume 60, Issue 6, Pages 957–972
DOI: https://doi.org/10.1134/S0037446619060041
Bibliographic databases:
Document Type: Article
UDC: 519.21
Language: Russian
Citation: A. A. Borovkov, “Integro-local theorems in boundary crossing problems for compound renewal processes”, Sibirsk. Mat. Zh., 60:6 (2019), 1229–1246; Siberian Math. J., 60:6 (2019), 957–972
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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