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Journal of Applied Mathematics and Stochastic Analysis
Volume 7, Issue 3, Pages 423-436
http://dx.doi.org/10.1155/S1048953394000341

Large deviations for unbounded additive functionals of a Markov process with discrete time (noncompact case)

Institute for Problems of Information Transmission, Moscow, Russia

Received 1 February 1993; Revised 1 June 1993

Copyright © 1994 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We combine the Donsker and Varadhan large deviation principle (l.d.p) for the occupation measure of a Markov process with certain results of Deuschel and Stroock, to obtain the l.d.p. for unbounded functionals. Our approach relies on the concept of exponential tightness and on the Puhalskii theorem. Three illustrative examples are considered.