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

Touati, Abderrahmen

Ann. Probab. 18, No. 1, 140-159 (1990).

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

MSC:

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

Keywords:

Harris recurrent Markov process; additive functionals; invariant measure; Skorokhod embedding technique; rate of almost sure convergence