Large Deviations for Markov Chains with Random Transitions

Abstract

This paper presents almost sure uniform large deviation principles for the empirical distributions and empirical processes of Markov chains with random transitions. The results are derived under assumptions that generalize assumptions earlier used for time-homogeneous chains. The rate functions for the skew chain are expressed in terms of the Donsker-Varadhan functional and relative entropy. The sample chain rates are different, but they have natural upper and lower bounds in terms of familiar rate functions.