On Large Deviation Property of Recurrence Times

TL;DR

This paper investigates the large deviation properties of recurrence times in mixing processes and proposes an entropy estimator based on recurrence times, with proven large deviation behavior for certain stationary and ergodic sources.

Contribution

It extends Ornstein and Weiss's work by establishing large deviation principles for recurrence times and introduces a new entropy estimator with proven large deviation properties.

Findings

Large deviation property established for a class of mixing processes.

Proposed entropy estimator based on recurrence times.

Large deviation behavior proved for stationary and ergodic sources.

Abstract

We extend the study by Ornstein and Weiss on the asymptotic behavior of the normalized version of recurrence times and establish the large deviation property for a certain class of mixing processes. Further, an estimator for entropy based on recurrence times is proposed for which large deviation behavior is proved for stationary and ergodic sources satisfying similar mixing conditions.