Loi fonctionnelle du logarithme itéré pour les processus de Markov récurrents. (Functional iterated logarithm law for recurrent Markov processes). (French) Zbl 0704.60025

Let X be a discrete- or continuous-parameter Harris recurrent Markov process. For additive functionals of X which are close to square integrable martingales with respect to the invariant measure of X, a functional law of the iterated logarithm is given. The proof is based on the Skorokhod embedding technique and the construction of an atom for a Harris chain. Two examples illustrate the use of the law obtained to get the rate of almost sure convergence of an estimator.
Reviewer: M.Iosifescu


60F15 Strong limit theorems
60J55 Local time and additive functionals
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