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January, 1990 Loi Fonctionnelle du Logarithme Itere Pour les Processus de Markov Recurrents
Abderrahmen Touati
Ann. Probab. 18(1): 140-159 (January, 1990). DOI: 10.1214/aop/1176990942


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.


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Abderrahmen Touati. "Loi Fonctionnelle du Logarithme Itere Pour les Processus de Markov Recurrents." Ann. Probab. 18 (1) 140 - 159, January, 1990.


Published: January, 1990
First available in Project Euclid: 19 April 2007

zbMATH: 0704.60025
MathSciNet: MR1043941
Digital Object Identifier: 10.1214/aop/1176990942

Primary: 60F15
Secondary: 60J55

Keywords: chaine atomique , fonctionnelle additive , loi du logarithme itere , Processus de Markov

Rights: Copyright © 1990 Institute of Mathematical Statistics


Vol.18 • No. 1 • January, 1990
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