A general correlation inequality and the Almost Sure Local Limit Theorem for random sequences in the domain of attraction of a stable law |
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Authors: | Rita Giuliano Zbigniew S Szewczak |
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Institution: | 1. Dipartimento di Matematica “L. Tonelli”, Università di Pisa, Largo Bruno Pontecorvo 5, I-56127 Pisa, Italy;2. Nicolaus Copernicus University, Faculty of Mathematics and Computer Science, ul. Chopina 12/18 87-100 Toruń, Poland |
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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∈(1,2). |
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Keywords: | primary 60F15 secondary 60E07 62H20 |
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