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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2018, Volume 15, Pages 475–502
DOI: https://doi.org/10.17377/semi.2018.15.041 (Mi semr932) 		 
This article is cited in 11 scientific papers (total in 11 papers)

Probability theory and mathematical statistics

Integro-local theorems for multidimensional compound renewal processes, when Cramer's condition holds. I

A. A. Mogulskiiab, E. I. Prokopenkoab

a Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia
b Novosibirsk State University, 1 Pirogova Str., 630090, Novosibirsk, Russia
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DOI: https://doi.org/10.17377/semi.2018.15.041
Abstract: In the work, which consists of 4 papers (the article and [15]–[17]), we obtain integro-local limit theorems in the phase space for multidimensional compound renewal processes, when Cramer's condition holds.
In the part I (the article) we consider the so-called first renewal process $\mathbf{Z}(t)$ in a regular region, which is an of analog Cramer's deviation region for random walk. The regular region includes normal and moderate deviations.
Keywords: compound multidimensional renewal process, first (second) renewal process, large deviations, integro-local limit theorems, renewal measure, Cramer's condition, deviation (rate) function, second deviation (rate) function.
Funding agency Grant number
Russian Science Foundation 18-11-00129
Received February 5, 2018, published May 4, 2018
Bibliographic databases:
Document Type: Article
UDC: 519.21
MSC: 60K05, 60F10
Language: Russian
Citation: A. A. Mogulskii, E. I. Prokopenko, “Integro-local theorems for multidimensional compound renewal processes, when Cramer's condition holds. I”, Sib. Èlektron. Mat. Izv., 15 (2018), 475–502
Citation in format AMSBIB
\Bibitem{MogPro18}
\by A.~A.~Mogulskii, E.~I.~Prokopenko
\paper Integro-local theorems for multidimensional compound renewal processes, when Cramer's condition holds. I
\jour Sib. \`Elektron. Mat. Izv.
\yr 2018
\vol 15
\pages 475--502
\mathnet{http://mi.mathnet.ru/semr932}
\crossref{https://doi.org/10.17377/semi.2018.15.041}
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