Journal of Applied Mathematics and Stochastic Analysis 
Volume 7 (1994), Issue 3, Pages 423-436
doi:10.1155/S1048953394000341

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

O. V. Gulinskii, Robert S. Lipster, and S. V. Lototskii

 Institute for Problems of Information Transmission, Moscow, Russia
Received 1 February 1993; Revised 1 June 1993

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.