摘要
设E={1,2,…,N},{(X_k,Y_k),k≥1}是在E×E中取值的随机向量序列,其中{Y_k,k≥1}是非齐次马氏链,对任意n≥2,(X_1,…,X_n)在给定(Y_1,…,Y_n)的情况下条件独立,且X_i的条件分布仅依赖于Y_i的值。设i∈E,S_n(i),Q_n(i)分别表示序列X_1,…,X_n与Y_1,…,Y_n中i的个数。本文用分析方法研究关于S_n(i)与Q_n(i)的强极限定理。
Let E = {1, …, N} and {(Xt,Yk), k ≥ 1} be a sequence of random vactors taking values in E×E, where {Yk,k ≥ 1} is anonhomogeneous Markov chain. For any n ≥ 2,X1,…,Xn are conditionally independent under the condition that (Y1,…,yn) is given and the conditional distribution of Xi depends only on the value of Yi .For i ∈ E, let Sn(i) and Qn(i) denote respectively the numbers of i in the sequences X1,…,Xnand Y1,…, Yn . In this paper ,by using an analytic method a strong limit theorem concerning Sn(i) and Qn(i) is established
基金
河北省自然科学基金
关键词
条件独立
强极限定理
随机变量
Conditional independence ,finite non-homogeneous Markov chain ,strong limit theorem.
