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.
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.
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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