一个关于马尔可夫链的极限定理(英文)

A Limit Theorem for Markov Chains

给出一个关于可列非齐次马尔可夫链M元状态序组出现频率的新形式的强极限定理,所得结论对任意可列非齐次马尔可夫链普遍成立.

Let {X_n, n≥0} be a Markov chain with state space S={1,2,…}, initial distribution q(1), q(2), …(1) and transition matrices P_n=(p_n(i,j)),i,j∈S,n=0,1,2,…(2) where p_n(i,j)=P(X_(n+1)=j|X_n=i). The purpose of this paper is to present a new strong limit theorem on the frequency of m-tuple of states which holds for arbitrary countable non-homogeneous Markov chains by using professor Liu wen's analytical method^([1]).