An empirical central limit theorem in L^1 for stationary sequences

Details An empirical central limit theorem in L^1 for stationary sequences An empirical central limit theorem in L^1 for stationary sequences

2008-12-15

arxiv.org/abs/0812.2839v1

Mathematics

Probability

20 pages

Scientific paper

In this paper, we derive asymptotic results for L^1-Wasserstein distance between the distribution function and the corresponding empirical distribution function of a stationary sequence. Next, we give some applications to dynamical systems and causal linear processes. To prove our main result, we give a Central Limit Theorem for ergodic stationary sequences of random variables with values in L^1. The conditions obtained are expressed in terms of projective-type conditions. The main tools are martingale approximations.

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