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

被引：2
|
作者：
Giuliano, Rita [1 ]
Szewczak, Zbigniew S. [2 ]
机构：
[1] Univ Pisa, Dipartimento Matemat L Tonelli, I-56127 Pisa, Italy
[2] Nicolaus Copernicus Univ, Fac Math & Comp Sci, PL-87100 Torun, Poland
来源：
STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2014年 / 124卷 / 04期
关键词：
Almost Sure Local Limit Theorem; Domain of attraction; Stable law; Characteristic function; Correlation inequality;
D O I：
10.1016/j.spa.2013.12.002
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
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 alpha-stable law, alpha is an element of (1, 2). (C) 2013 Elsevier B.V. All rights reserved.
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页码：1612 / 1626
页数：15
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