关于可列非齐次马氏链m元状态序组出现频率的一类强大数定律

A Class of Strong Laws of Large Numbers on Frequency of M-Tuple of State for Countable Non-Homogeneous Markov Chains

设｛Ｘｎ，ｎ≥０｝是可列非齐次马氏链，Ｓｎ（ｉ０…，ｉｍ－１，ω）表示ｍ元状态序组（ｉ０…，ｉｍ－１）在序列（Ｘ０，…，Ｘｍ－１），（Ｘ１，…，Ｘｍ），…，（Ｘｎ－１，…，Ｘｎ＋ｍ－２）中出现的次数．本文通过（Ｘｎ，ｎ≥０｝在Ｗｉｅｎｅｒ概率空间的一种实现，给出了关于Ｓｎ（ｉ０，…ｉｍ－１，ω）的一类对任意可列非齐次马氏链普遍成立的强大数定律．

Let {Xn,n≥0 }be a countable non-homogeneous Markov chain,and Sn(i0,…,im-1,ω)be the number of the m-tuple (i0,…,im-1)of states in the sequence of the m-dimensional random vectors (X,… ,Xm-1,), (X1, …,Xm),…, (Xn-1,…,Xn+m-2), In this paper,by use of a realization of(Xn,n≥0)in the Wieners probability space,a class of strong laws of large numbers on Sn(i0,…,im-1,ω)which hold for arbitrary countable non-homogeneous Markov chains are obtained.