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中文摘要：
研究树上二重非齐次马氏链随机转移概率的几何平均强极限定理和二重非齐次马氏链关于状态出现频率的强极限定理.首先引出了二重非齐次马氏链的概念,然后给出了一个引理,利用这个引理,建立了双根树上二重非齐次马氏链随机转移概率的用不等式表示的几何平均强极限定理,接着推出了二重非齐次马氏链关于状态序偶出现频率的用不等式表示的强极限定理;最后作为推论,得到树上有限非齐次马氏链随机转移概率的强极限定理.
英文摘要：
Some strong limit theorems relative to the geometric average of random transition probability for second-order nonhomogeneous Markov chains indexed by a tree were studied.The definition of the se-cond-order nonhomogeneous Markov chains was introduced to propose a lemma.According to the lemma,some strong limit theorems relative to the geometric average of random transition probability with inequality for second-order nonhomogeneous Markov chains indexed by a tree were established.Some strong limit theorems relative to occasional occurred frequency of states with inequality for second-order nonhomogeneous Markov chains indexed by a tree were deduced.As corollaries,some strong limit theorems for finite nonhomogeneous Markov chains indexed by a tree were achieved.
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