任意随机变量序列泛函及其随机变换的一类极限定理  

A Class of Strong limit Theorems for Functions of the Sequence of Arbitrary Random Variable and Their Random Transforms

作　　者：王康康[1] 马越[2] 

机构地区：[1]江苏科技大学数理学院,江苏镇江212003 [2]江苏大学京江学院,江苏镇江212013

出　　处：《数学的实践与认识》2008年第20期159-164,共6页Mathematics in Practice and Theory

基　　金：江苏省高校自然科学基础研究项目(07KJD110048)

摘　　要：采用鞅方法研究对任意随机变量序列普遍成立的强极限定理.并作为推论得到了m阶马氏过程,鞅序列,鞅差序列,独立随机变量序列的一类强极限定理.并把赌博系统的随机变换概念推广到任意随机变量序列的情况,得到任意随机变量序列随机选择与公平比的若干极限定理.Some strong limit theorems for the sequence of arbitrary random sequence are discussed by means of martingale method. As corollaries, a class of strong large number laws for m-order Markov chains, martingale difference sequence and the sequence of independent random variables are obtained. Moreover, the idea of random transformation of gambling system is extended to the sequence of arbitrary random variable, and as corollaries, some limit theorems for their random selection and random equitable ratios are obtained.

关 键 词：任意随机变量序列 马氏过程 鞅差序列 随机变换 随机公平比 强极限定理 

分 类 号：O211.4[理学—概率论与数理统计] O177[理学—数学]