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

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 $\alpha$--stable law, $\alpha \in (1,2)$.

References in corpus (1)

• A sharp correlation inequality with an application to almost sure local limit theorem

Cited by in corpus (1)

• Almost Sure Local Limit Theorem for the Dickman distribution