A Note for Estimation About Average Differential Entropy of Continuous Bounded Space-Time Random Field

In this paper, we mainly study the discrete approximation about average differential entropy of continuous bounded space-time random field. The estimation of differential entropy on random variable is a classic problem, and there are many related studies. Space-time random field is a theoretical extension of adding random variables to space-time parameters, but studies on discrete estimation of entropy on space-time random field are relatively few. The differential entropy forms of continuous bounded space-time random field and discrete estimations are discussed, and three estimation forms of differential entropy in the case of random variables are generated in this paper. Furthermore, it is concluded that under the condition that the entropy estimation formula after space-time segmentation converges with probability 1, the average entropy in the bounded space-time region can also converge with probability 1, and three generalized entropies are verified respectively. In addition, we also carried out numerical experiments on the convergence of average entropy estimation based on parameters, and the numerical results are consistent with the theoretical results, which indicting further study of the average entropy estimation problem of space-time random fields is significant in the future.