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Article Dans Une Revue Electronic Journal of Probability Année : 2014

A Sequential Empirical Central Limit Theorem for Multiple Mixing Processes with Application to B-Geometrically Ergodic Markov Chains

Résumé

We investigate the convergence in distribution of sequential empirical processes of dependent data indexed by a class of functions F. Our technique is suitable for processes that satisfy a multiple mixing condition on a space of functions which differs from the class F. This situation occurs in the case of data arising from dynamical systems or Markov chains, for which the Perron-Frobenius or Markov operator, respectively, has a spectral gap on a restricted space. We provide applications to iterative Lipschitz models that contract on average.

Dates et versions

hal-00802979 , version 1 (20-03-2013)

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Herold Dehling, Olivier Durieu, Marco Tusche. A Sequential Empirical Central Limit Theorem for Multiple Mixing Processes with Application to B-Geometrically Ergodic Markov Chains. Electronic Journal of Probability, 2014, 19 (87), pp.1-26. ⟨10.1214/EJP.v19-3216⟩. ⟨hal-00802979⟩
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