树上路径过程的随机路径条件概率的强极限定理

摘要

本文研究了树上路径过程随机转移概率和状态序偶出现频率的强极限定理。通过利用若干重要不等式，获得了树上路径过程的随机路径条件概率用不等式表示的几何平均强极限定理以及树上路径过程关于状态序偶出现频率的用不等式表示的强极限定理，所得结果推广了树上马氏链及非齐次马氏链中的结果。%In this paper, some strong limit theorems relative to the geometric average and occurred frequency of states for path process indexed by a tree were studied. The definition of the path process indexed by a tree was introduced to propose a lemma. Some strong limit theorems relative to the geometric average of random path conditional probability with inequality for path process indexed by a tree was established, and some strong limit theorems relative to occasional occurred frequency of states with inequality for path process indexed by a tree was deduced. As corollary, random conditional probability for nonhomogeneous Markov chains indexed by a tree was achieved.