Electronic Journal of Probability

A sequential empirical CLT for multiple mixing processes with application to $\mathcal{B}$-geometrically ergodic Markov chains

Herold Dehling, Olivier Durieu, and Marco Tusche

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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.

Article information

Electron. J. Probab. Volume 19 (2014), paper no. 87, 26 pp.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60F05: Central limit and other weak theorems
Secondary: 60F17: Functional limit theorems; invariance principles 60G10: Stationary processes 62G30: Order statistics; empirical distribution functions 60J05: Discrete-time Markov processes on general state spaces

Multivariate Sequential Empirical Processes Limit Theorems Multiple Mixing Spectral Gap Dynamical Systems Markov chain Change-Point Problems

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Dehling, Herold; Durieu, Olivier; Tusche, Marco. A sequential empirical CLT for multiple mixing processes with application to $\mathcal{B}$-geometrically ergodic Markov chains. Electron. J. Probab. 19 (2014), paper no. 87, 26 pp. doi:10.1214/EJP.v19-3216. https://projecteuclid.org/euclid.ejp/1465065729.

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