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Sibirsk. Mat. Zh., 2018, Volume 59, Number 4, Pages 736–758 (Mi smj3007)  

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

A. A. Borovkov, A. A. Mogulskii

Sobolev Institute of Mathematics, Novosibirsk, Russia

Abstract: We prove the statements that are formulated in the first part of this paper. As an auxiliary proposition, we establish an integro-local theorem for the renewal measure of a two-dimensional random walk.

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).


DOI: https://doi.org/10.17377/smzh.2018.59.402

Full text: PDF file (363 kB)
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English version:
Siberian Mathematical Journal, 2018, 59:4, 578–597

Bibliographic databases:

UDC: 519.21
MSC: 35R30
Received: 11.12.2017

Citation: A. A. Borovkov, A. A. Mogulskii, “Integro-local limit theorems for compound renewal processes under Cramér's condition. II”, Sibirsk. Mat. Zh., 59:4 (2018), 736–758; Siberian Math. J., 59:4 (2018), 578–597

Citation in format AMSBIB
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\paper Integro-local limit theorems for compound renewal processes under Cram\'er's condition.~II
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\pages 736--758
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