Identification of the rate function for large deviations of an irreducible markov chain

Abstract

For an irreducible Markov chain (Xn)n≥0 we identify the rate function governing the large deviation estimation of empirical mean 1/n Σn-1k=0 f(Xk) by means of the Donsker-Varadhan’s entropy. That allows us to obtain the lower bound of large deviations for the empirical measure 1/n Σn-1k=0 δXk in full generality. © 2009 Applied Probability Trust.