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2014 A sequential empirical CLT for multiple mixing processes with application to $\mathcal{B}$-geometrically ergodic Markov chains
Herold Dehling, Olivier Durieu, Marco Tusche
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Electron. J. Probab. 19: 1-26 (2014). DOI: 10.1214/EJP.v19-3216

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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Herold Dehling. Olivier Durieu. Marco Tusche. "A sequential empirical CLT for multiple mixing processes with application to $\mathcal{B}$-geometrically ergodic Markov chains." Electron. J. Probab. 19 1 - 26, 2014. https://doi.org/10.1214/EJP.v19-3216

Information

Accepted: 20 September 2014; Published: 2014
First available in Project Euclid: 4 June 2016

zbMATH: 1302.60047
MathSciNet: MR3263644
Digital Object Identifier: 10.1214/EJP.v19-3216

Subjects:
Primary: 60F05
Secondary: 60F17 , 60G10 , 60J05 , 62G30

Keywords: Change-point problems , dynamical systems , limit theorems , Markov chain , Multiple Mixing , Multivariate Sequential Empirical Processes , spectral gap

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Vol.19 • 2014
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