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

doi:10.1007/s10473-024-0521-4

数学物理学报(英文版) ›› 2024, Vol. 44 ›› Issue (5): 1984-1996.doi: 10.1007/s10473-024-0521-4

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

Zhanjie SONG^1,2, Jiaxing ZHANG^3,4,†

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;
4. Tianjin Key Laboratory of Brain-Inspired Intelligence Technology, Tianjin 300072, China

收稿日期:2022-05-25 修回日期:2024-05-25 出版日期:2024-10-25 发布日期:2024-10-22
通讯作者: †Jiaxing ZHANG, E-mail,: 2017233010@tju.edu.cn
作者简介:Zhanjie SONG, E-mail,: zhanjiesong@tju.edu.cn
基金资助:
Shenzhen sustainable development project: KCXFZ 20201221173013036 and the National Natural Science Foundation of China (91746107).

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

Zhanjie SONG^1,2, Jiaxing ZHANG^3,4,†

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;
4. Tianjin Key Laboratory of Brain-Inspired Intelligence Technology, Tianjin 300072, China

Received:2022-05-25 Revised:2024-05-25 Online:2024-10-25 Published:2024-10-22
Contact: †Jiaxing ZHANG, E-mail,: 2017233010@tju.edu.cn
About author:Zhanjie SONG, E-mail,: zhanjiesong@tju.edu.cn
Supported by:
Shenzhen sustainable development project: KCXFZ 20201221173013036 and the National Natural Science Foundation of China (91746107).

摘要/Abstract

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

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

中图分类号:

94A17

Zhanjie SONG, Jiaxing ZHANG. ESTIMATION OF AVERAGE DIFFERENTIAL ENTROPY FOR A STATIONARY ERGODIC SPACE-TIME RANDOM FIELD ON A BOUNDED AREA^*[J]. 数学物理学报(英文版), 2024, 44(5): 1984-1996.

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^*

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

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