证明中应用了研究马尔可夫链强极限定理的一种新的分析方法。
In the proof a new analytic technique in the study of the strong limit theorems for Markov chains is applied.
通过对QBD过程某些条件的限定，应用马尔可夫更新定理，得出在一定合理的条件下，当水平趋于无穷时的尾概率的几何衰变。
Applying the Markov renewal theorem, it is shown that certain reasonable conditions of the QBD process lead to the geometric decay of the tail probabilities as the level goes to infinity.
本文的目的是要给出关于可列非齐次马尔可夫链M元状态序组出现频率的一类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。
The purpose of this paper is to present a class of new strong limit theorems on the frequency ofm-tuple of states for arbitrary countable non-homogeneous Markov chains.
本文给出一个将DHMM转化为齐次马尔可夫链的定理，该定理提供了利用在理论上比较完善的齐次马尔可夫链来研究DHMM的一个方法。
In this paper a theorem on translating DHMM into Homogeneous Markov Chain is presented. The theorem offers a method of using Homogeneous Markov Cain which is perfect in theory to study DHMM.
首先在引理中得出了隐非齐次马尔可夫模型的一些性质，从而导出了隐非齐次马尔可夫模型的三元函数一类平均值的强极限定理。
At first some properties on nonhomogeneous Markov models are obtained in the lemma, then a limit theorem for the average of the three variables function of hidden nonhomogeneous Markov model is given.
主题包括测度论，极限定理，包围概率和期望，耦合和斯坦的方法，鞅，马尔可夫链，更新理论，和布朗运动。
Topics include measure theory, limit theorems, bounding probabilities and expectations, coupling and Stein's method, martingales, Markov chains, renewal theory, and Brownian motion.
主题包括测度论，极限定理，包围概率和期望，耦合和斯坦的方法，鞅，马尔可夫链，更新理论，和布朗运动。
Topics include measure theory, limit theorems, bounding probabilities and expectations, coupling and Stein's method, martingales, Markov chains, renewal theory, and Brownian motion.
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