任意随机序列随机条件概率调和平均的一类强偏差定理

Strong deviation theorems for the harmonic mean of the random conditional probabilities for the arbitrary stochastic sequence

主要研究任意随机序列随机条件概率调和平均的a.s.收敛的强偏差定理.在证明中采用了一种把网微分法与条件矩母函数相结合应用于强极限定理研究的新途径.作为推论,得到任意随机序列随机条件概率的一个公平比的强极限定理,并将已有的结果加以推广.

In this paper, we study the strong limit theorems on the a.s. convergence for the harmonic mean of the arbitrary stochastic sequence. In the proof, we apply the tools of the conditional moment generating functions and the differentiation on a net to the study of strong limit theorems for the arbitrary stochastic sequence. As cor- ollaries, a limit theorem for fair ratio of the arbitrary stochastic sequence is obtained. Moreover, the result which has been obtained is generalized.