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

Abstract : 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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Preprints, Working Papers, ...
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Contributor : Sophie Dede <>
Submitted on : Monday, December 15, 2008 - 3:01:10 PM
Last modification on : Friday, March 27, 2020 - 4:01:49 AM
Long-term archiving on: : Tuesday, June 8, 2010 - 5:13:31 PM


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  • HAL Id : hal-00347334, version 1
  • ARXIV : 0812.2839


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