连续随机序列样本熵的强偏差定理

A Strong Deviation Theorem for Continuous Random Sequenc Sample Entropy

设{X_n,n≥1}是连续随机序列,其联合分布密度为g_n(x_1,…,x_n),f_k(x_k)是X_k的边缘分布密度。利用关于乘积分布密度sum from n to k=1 f_k(x_k)的相对熵和相对熵率的概念,建立了连续随机序列关于样本微分熵的一类强偏差定理。

Let {Xn,n≥1} be continuous random sequences with the joint distribution gn（X1,…,Xn）. In this pa-per a strong deviation theorem for continuous random sequenses sample differential entropy is established by using the notion of sample relative entropy rate and relative entropy with respect to reference product distribution nПk=1 fk（Xk） ,where fk（Xk） is the marginal distribution of Xk.