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

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-00802979
Contributor : Olivier Durieu <>
Submitted on : Wednesday, March 20, 2013 - 5:07:50 PM
Last modification on : Thursday, February 7, 2019 - 4:57:00 PM

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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, Institute of Mathematical Statistics (IMS), 2014, 19 (87), pp.1-26. ⟨10.1214/EJP.v19-3216⟩. ⟨hal-00802979⟩

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