## The Annals of Probability

### Loi Fonctionnelle du Logarithme Itere Pour les Processus de Markov Recurrents

Abderrahmen Touati

#### Abstract

Let $X$ be a Harris recurrent Markov process (in discrete or continuous time). We give a functional law of the iterated logarithm for the additive functionals of $X$ which are (close to) square integrable martingales with respect to the invariant measure of $X$. The proof is based on the Skorokhod embedding technique and the construction of an atom for a Harris chain. In contrast with the positive recurrent case, "the suitable normalizations" are random in the null recurrent case. Moreover it is shown from two examples how to use the law of the iterated logarithm to get the rate of almost sure convergence of an estimator.

#### Article information

Source
Ann. Probab., Volume 18, Number 1 (1990), 140-159.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176990942

Digital Object Identifier
doi:10.1214/aop/1176990942

Mathematical Reviews number (MathSciNet)
MR1043941

Zentralblatt MATH identifier
0704.60025

JSTOR