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Theory of Probability and Mathematical Statistics



THE UNIFORM CLT FOR EMPIRICAL ESTIMATOR OF A GENERAL STATE SPACE SEMI-MARKOV KERNEL INDEXED BY FUNCTIONS

S. BOUZEBDA, N. LIMNIOS

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Abstract: In this paper we mainly deal with the uniform CLT for empirical estimator of a general state space semi-Markov process indexed by functions under the uniformly integrable entropy condition. A way to describe the uniform CLT is to translate the problem into martingale diference sequences to obtain the desired results.

Keywords: Semi-Markov process, semi-Markov kernel, empirical estimator, uniform central limit theorem, invariance principle.

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