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Sibirsk. Mat. Zh., 2018, Volume 59, Number 3, Pages 491–513 (Mi smj2989)  

This article is cited in 5 scientific papers (total in 5 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

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).


DOI: https://doi.org/10.17377/smzh.2018.59.302

Full text: PDF file (385 kB)
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English version:
Siberian Mathematical Journal, 2018, 59:3, 383–402

Bibliographic databases:

UDC: 519.21
MSC: 35R30
Received: 12.12.2017

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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\paper Integro-local limit theorems for compound renewal processes under Cram\'er's condition.~I
\jour Sibirsk. Mat. Zh.
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\vol 59
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\pages 491--513
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\crossref{https://doi.org/10.17377/smzh.2018.59.302}
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\jour Siberian Math. J.
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\vol 59
\issue 3
\pages 383--402
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    This publication is cited in the following articles:
    1. A. A. Mogulskii, E. I. Prokopenko, “Integro-lokalnye teoremy dlya mnogomernykh obobschennykh protsessov vosstanovleniya pri momentnom uslovii Kramera. I”, Sib. elektron. matem. izv., 15 (2018), 475–502  mathnet  crossref
    2. A. A. Mogulskii, E. I. Prokopenko, “Integro-lokalnye teoremy dlya mnogomernykh obobschennykh protsessov vosstanovleniya pri momentnom uslovii Kramera. II”, Sib. elektron. matem. izv., 15 (2018), 503–527  mathnet  crossref
    3. A. A. Mogulskii, E. I. Prokopenko, “Integro-lokalnye teoremy dlya mnogomernykh obobschennykh protsessov vosstanovleniya pri momentnom uslovii Kramera. III”, Sib. elektron. matem. izv., 15 (2018), 528–553  mathnet  crossref
    4. A. A. Borovkov, A. A. Mogulskii, “Integro-local limit theorems for compound renewal processes under Cramér's condition. II”, Siberian Math. J., 59:4 (2018), 578–597  mathnet  crossref  crossref  isi  elib
    5. A. A. Mogulskii, “Lokalnye teoremy dlya arifmeticheskikh obobschennykh protsessov vosstanovleniya pri vypolnenii usloviya Kramera”, Sib. elektron. matem. izv., 16 (2019), 21–41  mathnet  crossref
  • Сибирский математический журнал Siberian Mathematical Journal
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