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


 
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1. Title Title of document A sequential empirical CLT for multiple mixing processes with application to $\mathcal{B}$-geometrically ergodic Markov chains
 
2. Creator Author's name, affiliation, country Herold Dehling; Ruhr-Universität Bochum; Germany
 
2. Creator Author's name, affiliation, country Olivier Durieu; Université de Tours; France
 
2. Creator Author's name, affiliation, country Marco Tusche; Ruhr-Universität Bochum & Université de Tours; Germany
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Multivariate Sequential Empirical Processes; Limit Theorems; Multiple Mixing; Spectral Gap; Dynamical Systems; Markov chain; Change-Point Problems
 
3. Subject Subject classification 60F05; 60F17; 60G10; 62G30; 60J05
 
4. Description 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) German Science Foundation
 
7. Date (YYYY-MM-DD) 2014-09-20
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/3216
 
10. Identifier Digital Object Identifier 10.1214/EJP.v19-3216
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 19
 
12. Language English=en en
 
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