关于滑动相对熵的若干极限性质

On Some Limit Properties of Moving Relative Entropy

引入滑动似然比和滑动相对熵等概念,讨论了滑动相对熵的若干渐近性质.主要结果是,获得了随机变量任意状态的相对频率与滑动相对熵之间的关系,并且给出了滑动相对熵基于相对频率的上界的估计.作为推论,得到了随机序列滑动平均的强大数定理.

In this paper,the moving likelihood ratio and moving relative entropy are introduced,and some asymptotic properties of the moving relative entropy are discussed.The main result is that we obtain the relationship between the relative frequency and the moving relative entropy of random variables in any state,and give the estimation of the upper bound of the moving relative entropy based on the relative frequency.As a corollary,the strong number theorem for moving average of random sequences is obtained.