Empirical processes of multidimensional systems with multiple mixing properties

Herold Dehling and Olivier Durieu

Stochastic Processes and their Applications, 2011, vol. 121, issue 5, 1076-1096

Abstract: 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.

Keywords: Multivariate; empirical; processes; Multiple; mixing; property; Dynamical; systems; Spectral; gap; property (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (4)

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