ESTIMATION OF AVERAGE DIFFERENTIAL ENTROPY FOR A STATIONARY ERGODIC SPACE-TIME RANDOM FIELD ON A BOUNDED AREA*

doi:10.1007/s10473-024-0521-4

Abstract

Abstract: In this paper, we mainly discuss a discrete estimation of the average differential entropy for a continuous time-stationary ergodic space-time random field. By estimating the probability value of a time-stationary random field in a small range, we give an entropy estimation and obtain the average entropy estimation formula in a certain bounded space region. It can be proven that the estimation of the average differential entropy converges to the theoretical value with a probability of 1. In addition, we also conducted numerical experiments for different parameters to verify the convergence result obtained in the theoretical proofs.

Key words: differential entropy, stationary, ergodicity, space-time random field, time series

CLC Number:

94A17

Zhanjie SONG, Jiaxing ZHANG. ESTIMATION OF AVERAGE DIFFERENTIAL ENTROPY FOR A STATIONARY ERGODIC SPACE-TIME RANDOM FIELD ON A BOUNDED AREA^*[J].Acta mathematica scientia,Series B, 2024, 44(5): 1984-1996.

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ESTIMATION OF AVERAGE DIFFERENTIAL ENTROPY FOR A STATIONARY ERGODIC SPACE-TIME RANDOM FIELD ON A BOUNDED AREA^*

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