随机序列的变换及其局部强收敛性

摘要

The notion of the stopping transform for arbitrary stochastic sequence is introduced. Some limit theorems for local convergence of such transforms and strong law of large numbers are studied by means of martingale convergence theorem together with the theorem of infinite products, as corollaries, some strong law of large numbers on gambling system are also obtained.%本文引入任意随机变量序列停时变换的概念,利用截尾方法构造几乎处处收敛的鞅结合无穷乘积定理,讨论了变换的局部收敛性及强大数定理,作为推论得到了关于赌博系统的若干强极限定理.