A general correlation inequality and the Almost Sure Local Limit Theorem for random sequences in the domain of attraction of a stable law

Rita Giuliano; Zbigniew S. Szewczak

doi:10.1016/j.spa.2013.12.002

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arXiv · 1312.2208

A general correlation inequality and the Almost Sure Local Limit Theorem for random sequences in the domain of attraction of a stable law

Rita Giuliano·Zbigniew S. Szewczak

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Abstract

In the present paper we obtain a new correlation inequality and use it for the purpose of extending the theory of the Almost Sure Local Limit Theorem to the case of lattice random sequences in the domain of attraction of a stable law. In particular, we prove ASLLT in the case of the normal domain of attraction of $α$--stable law, $α\in(1,2)$.

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Rita Giuliano, Zbigniew S. Szewczak. 2013-12-08. A general correlation inequality and the Almost Sure Local Limit Theorem for random sequences in the domain of attraction of a stable law. https://doi.org/10.1016/j.spa.2013.12.002

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