Large Deviations Principle in Finite and Homogeneous Markov Chains.

 Marco Antônio GIACOMELLI[1] 

 

§    ABSTRACT: Cramer-Chernoff’s Large Deviations Principle (LDP) was create in 1952 for sequence of random variables that are independent and identically distributed. Extensions it has been made for random variables with some kind of stochastic dependence. This paper is restricted to the context of finite and homogeneous Markov chains. Some definitions and results are given initially for use later. The objective is to analyse three situations where LDP is applied: the sample mean, the empirical measure and the pairempirical measure. The central reference is Ellis (1985), who calls mean, empirical measure and pair empirical measure by level 1, level 2 and level 3 sums, respectively.

§    KEYWORDS: Large Deviations Principle, sample mean in Markov Chains, empirical measure in Markov Chains.

 



1 Departamento de Estat´ıtica da Universidade Federal do Rio Grande do Sul, Porto Alegre-RS, e-mail:giacomo@mat.ufrgs.br