可列非齐次马氏链的强极限定理

Strong Limit Theorems of Countable Nonhomogeneous Markov Chain

设 { Xn,n≥ 0 }是状态空间 S={ 1 ,2 ,3,… }上具有初始分布 q( i)和转移概率 Pn=pn( i,j) =P( Xn=j|Xn- 1 =i)的可列非齐次马氏链 ,其中 i,j∈ S.利用马氏链的特性和网微分的方法讨论 { Xn,n≥ 0 }的级数收敛性 ,建立了若干强极限定理和强大数定律 .

Let {X n,n≥0} be a nonhomogeneous Markov chain with the state space S={1,2,…}and the initial distribution q(i),the transition probability P n=p n(i,j)=P(X n=j｜X n-l =i),where i,j∈S.The convergence of series on {X n,n≥0} was discussed by the property on Markov chain and the differentiation on a net.Some strong limit theorems and strong laws of large numbers are obtained.