On the central and local limit theorem for martingale difference sequences

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Let $(Ω, \A, μ)$ be a Lebesgue space and $T$ an ergodic measure preserving automorphism on $Ω$ with positive entropy. We show that there is a bounded and strictly stationary martingale difference sequence defined on $Ω$ with a common non-degenerate lattice distribution satisfying the central limit theorem with an arbitrarily slow rate of convergence and not satisfying the local limit theorem. A similar result is established for martingale difference sequences with densities provided the entropy is infinite. In addition, the martingale difference sequence may be chosen to be strongly mixing.
Accepte pour publication dans Stochastics and Dynamics

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Probability, 60F99, 28D05

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http://salesiana.dossiersoluciones.com/handle/123456789/70305

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0403008
 http://arxiv.org/abs/math/0403008

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arXiv