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

作者：Giuliano Rita^*; Szewczak Zbigniew S

来源：Stochastic Processes and Their Applications, 2014, 124(4): 1612-1626.

DOI：10.1016/j.spa.2013.12.002

• Almost Sure Local Limit Theorem
• Domain of attraction
• Stable law
• Characteristic function
• Correlation inequality

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).

• 出版日期2014-4