A Sequential Empirical Central Limit Theorem for Multiple Mixing Processes with Application to B-Geometrically Ergodic Markov Chains - Archive ouverte HAL Access content directly
Journal Articles Electronic Journal of Probability Year : 2014

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.

Dates and versions

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

Identifiers

Cite

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⟩
203 View
0 Download

Altmetric

Share

Gmail Facebook X LinkedIn More