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Sibirskii Matematicheskii Zhurnal, 2018, Volume 59, Number 3, Pages 491–513
DOI: https://doi.org/10.17377/smzh.2018.59.302 (Mi smj2989) 		 
This article is cited in 22 scientific papers (total in 22 papers)

Integro-local limit theorems for compound renewal processes under Cramér's condition. I

A. A. Borovkov, A. A. Mogulskii

Sobolev Institute of Mathematics, Novosibirsk, Russia
Full-text PDF (385 kB) Citations (22)
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DOI: https://doi.org/10.17377/smzh.2018.59.302
Abstract: We obtain integro-local limit theorems in the phase space for compound renewal processes under Cramér's moment condition. These theorems apply in a domain analogous to Cramér's zone of deviations for random walks. It includes the zone of normal and moderately large deviations. Under the same conditions we establish some integro-local theorems for finite-dimensional distributions of compound renewal processes.
Keywords: compound renewal process, large deviations, integro-local theorem, renewal measure, Cramér's condition, deviation function, second deviation function.
Funding agency Grant number
Russian Foundation for Basic Research 18-01-00101
The authors were partially supported by the Russian Foundation for Basic Research (Grant 18-01-00101).
Received: 12.12.2017
English version:
Siberian Mathematical Journal, 2018, Volume 59, Issue 3, Pages 383–402
DOI: https://doi.org/10.1134/S0037446618030023
Bibliographic databases:
Document Type: Article
UDC: 519.21
MSC: 35R30
Language: Russian
Citation: A. A. Borovkov, A. A. Mogulskii, “Integro-local limit theorems for compound renewal processes under Cramér's condition. I”, Sibirsk. Mat. Zh., 59:3 (2018), 491–513; Siberian Math. J., 59:3 (2018), 383–402
Citation in format AMSBIB
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    This publication is cited in the following 22 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Сибирский математический журнал Siberian Mathematical Journal
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