离散随机序列加权和的若干极限定理

Some limit behavior for weighted sums of discrete random variables

设{X_n,n≥0}是任意离散随机变量序列,{a_(nk),0≤k≤n,n≥0}.是一常数阵列,我们引入随机序列渐近对数似然比的概念,作为表征随机序列的真实概率测度P与参考测度Q之间的差异的度量,用分析方法,得到了随机序列Jamison型加权和的若干随机偏差定理.

Consider {Xn, n ≥0} be a sequence of arbitrary discrete random variables and {ank, 0 ≤ k ≤ n, n ≤0} an arrary of constants, we introduce the notion of asymptotic log-likelihood ratio of stochastic sequences, as a measure of dissimilarity between true probability measure P and reference measure Q, and establish some strong deviation theorems for the Jamison type weighted sums random variables by means of analytical method.