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.