On a waiting-time result of Kontoyiannis: mixing or decoupling?

TL;DR

This paper extends the theoretical understanding of waiting-time estimations for cross entropy between independent stochastic processes by introducing lower decoupling conditions, broadening the applicability beyond traditional mixing assumptions.

Contribution

It replaces the $\psi$-mixing condition in Kontoyiannis's theorem with a lower decoupling condition, significantly extending the theorem's validity.

Findings

Extended waiting-time estimation validity under lower decoupling

Broadened applicability beyond $\psi$-mixing processes

Provided new conditions for cross entropy estimation

Abstract

We introduce conditions of lower decoupling to the study of waiting-time estimations of the cross entropy between two mutually independent stationary stochastic processes. Although similar decoupling conditions have been used in the literature on large deviations and statistical mechanics, they appear largely unexplored in information theory. Building on a result of Kontoyiannis, namely Theorem 4 in [Kontoyiannis, J. Theor. Probab., 1998], and replacing the $\psi$-mixing condition in this result with a lower decoupling condition, we considerably extend the validity of waiting-time estimation of cross entropy.