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Sib. Èlektron. Mat. Izv., 2019, Volume 16, Pages 1–20 (Mi semr1043)  

Probability theory and mathematical statistics

Large deviations for processes on half-line: Random Walk and Compound Poisson Process

F. C. Klebanera, A. A. Mogulskiib

a School of Mathematical Sciences, Monash University, Australia
b Sobolev Institute of Mathematics, pr. Koptyuga, 4, Novosibirsk, 630090, Russia

Abstract: We establish, under the Cramer exponential moment condition in a neighbourhood of zero, the Extended Large Deviation Principle for the Random Walk and the Compound Poisson processes in the metric space $\mathbb{V}$ of functions of finite variation on $[0,\infty)$ with the modified Borovkov metric.

Keywords: Large Deviations, Random Walk, Compound Poisson Process, Cramer's condition, rate function, Extended Large Deviation Principle.

Funding Agency Grant Number
Russian Foundation for Basic Research 18-01-00101_а
Siberian Branch of Russian Academy of Sciences I.1.3., project No. 0314-2016-0008
Australian Research Council DP150103588
This research was supported by the Russian Fund for Fundamental Research (projects number 18-01-00101$\backslash$18), by the program of fundamental scientific researches of the SB RAS No. I.1.3., project No. 0314-2016-0008 and the Australian Research Council Grant DP150103588.


DOI: https://doi.org/10.33048/semi.2019.16.001

Full text: PDF file (206 kB)
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Bibliographic databases:

UDC: 519.21
MSC: 60F10, 60G50, 60H10, 60J60
Received July 2, 2018, published January 24, 2019
Language:

Citation: F. C. Klebaner, A. A. Mogulskii, “Large deviations for processes on half-line: Random Walk and Compound Poisson Process”, Sib. Èlektron. Mat. Izv., 16 (2019), 1–20

Citation in format AMSBIB
\Bibitem{KleMog19}
\by F.~C.~Klebaner, A.~A.~Mogulskii
\paper Large deviations for processes on half-line: Random Walk and Compound Poisson Process
\jour Sib. \`Elektron. Mat. Izv.
\yr 2019
\vol 16
\pages 1--20
\mathnet{http://mi.mathnet.ru/semr1043}
\crossref{https://doi.org/10.33048/semi.2019.16.001}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000462268100001}


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