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

Sophie Dede (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

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.

Mots clés: Wasserstein distance; empirical distribution function; central limit theorem; stationary sequences; Wasserstein distance.

Domaines: Probabilités [math.PR]

Sophie Dede. An empirical central limit theorem in L^1 for stationary sequences.. 2008. ⟨hal-00347334⟩