Empirical processes of multidimensional systems with multiple mixing properties
We establish a multivariate empirical process central limit theorem for stationary -valued stochastic processes (Xi)i>=1 under very weak conditions concerning the dependence structure of the process. As an application, we can prove the empirical process CLT for ergodic torus automorphisms. Our results also apply to Markov chains and dynamical systems having a spectral gap on some Banach space of functions. Our proof uses a multivariate extension of the techniques introduced by Dehling et al. (2009) [9] in the univariate case. As an important technical ingredient, we prove a 2pth moment bound for partial sums in multiple mixing systems.
Year of publication: |
2011
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Authors: | Dehling, Herold ; Durieu, Olivier |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 121.2011, 5, p. 1076-1096
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Publisher: |
Elsevier |
Keywords: | Multivariate empirical processes Multiple mixing property Dynamical systems Spectral gap property |
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