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

Giampaolo Cristadoro, Mirko Degli Esposti, Vojkan Jakšić and Renaud Raquépas

Stochastic Processes and their Applications, 2023, vol. 166, issue C

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 (1998), and replacing the ψ-mixing condition in this result with a lower decoupling condition, we considerably extend the validity of waiting-time estimation of cross entropy.

Keywords: Cross entropy; Estimator; Waiting time; Decoupled measure; One-sided shift (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.spa.2023.09.009

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