On Asymptotic Equipartition Property for Stationary Process of Moving Averages

Abstract

Let {Xn}n∈Z be a stationary process with values in a finite set. In this paper, we present a moving average version of the Shannon–McMillan–Breiman theorem; this generalize the corresponding classical results. A sandwich argument reduced the proof to direct applications of the moving strong law of large numbers. The result generalizes the work by Algoet et. al., while relying on a similar sandwich method. It is worth noting that, in some kind of significance, the indices an and ϕ(n) are symmetrical, i.e., for any integer n, if the growth rate of (an)n∈Z is slow enough, all conclusions in this article still hold true.

Keywords

• ergodic
• stationary processes
• asymptotic equipartition property
• sandwich argument