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

作　　者：Zhanjie SONG Jiaxing ZHANG 宋占杰;张家兴(Georgia Tech Shenzhen Institute,Tianjin University,Shenzhen,518055,China;Tianjin Key Laboratory of Brain-Inspired Intelligence Technology,Tianjin,300072,China;School of Mathematics,Tianjin University,Tianjin,300354,China)

机构地区：[1]Georgia Tech Shenzhen Institute,Tianjin University,Shenzhen,518055,China [2]Tianjin Key Laboratory of Brain-Inspired Intelligence Technology,Tianjin,300072,China [3]School of Mathematics,Tianjin University,Tianjin,300354,China

出　　处：《Acta Mathematica Scientia》2024年第5期1984-1996,共13页数学物理学报（B辑英文版）

基　　金：supported by the Shenzhen sustainable development project:KCXFZ 20201221173013036 and the National Natural Science Foundation of China(91746107).

摘　　要：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.

关 键 词：differential entropy STATIONARY ERGODICITY space-time random field time series 

分 类 号：O211.6[理学—概率论与数理统计]