有界区域上静态遍历时空随机场的平均微分熵估算

IF 1.2 4区数学 Q1 MATHEMATICS

Acta Mathematica Scientia Pub Date : 2024-08-27 DOI:10.1007/s10473-024-0521-4

Zhanjie Song, Jiaxing Zhang

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引用次数: 0

摘要

本文主要讨论连续时静态遍历时空随机场的平均微分熵的离散估计。通过估计时静态随机场在一个小范围内的概率值，我们给出了一个熵估计值，并得到了在某个有界空间区域内的平均熵估计公式。此外，我们还对不同参数进行了数值实验，以验证理论证明中得到的收敛结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Estimation of average differential entropy for a stationary ergodic space-time random field on a bounded area

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.

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来源期刊

Acta Mathematica Scientia 数学-数学

CiteScore

2.00

自引率

10.00%

发文量

2614

审稿时长

6 months

期刊介绍： Acta Mathematica Scientia was founded by Prof. Li Guoping (Lee Kwok Ping) in April 1981. The aim of Acta Mathematica Scientia is to present to the specialized readers important new achievements in the areas of mathematical sciences. The journal considers for publication of original research papers in all areas related to the frontier branches of mathematics with other science and technology.