This article is cited in 9 papers

The large deviation principle for a compound Poisson process

A. A. Mogul'skiĭ<sup>ab

a</sup> Sobolev Institute of Mathematics, Novosibirsk, Russia
^b Novosibirsk State University, Novosibirsk, Russia

Abstract: For a compound Poisson process, under the moment Cramér condition, the extended large deviation principle is established in the space of functions of bounded variation with the Borovkov metric.

Key words: compound Poisson process, compound renewal process, Cramér condition, deviation rate function, large deviation principle, extended large deviation principle, function of bounded variation, Borovkov metric, Chebyshev-type inequality.

UDC: 519.21

Received: 12.05.2015

DOI: 10.17377/mattrudy.2016.19.205

 English version: Siberian Advances in Mathematics, 2017, 27:3, 160–186

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