利用鞅的概念，得到了该模型下的最终破产概率、盈余首次和末次达到给定水平时刻的分布。
Using the notion of martingale, the paper obtains the ultimate ruin probability and the distributions of the first and the last arrival time of a given level.
本章主要通过递推方法和鞅方法得出生存概率所满足的积分方程以及破产概率上界。
By recursive method and Martingale method, we derive the integral equation for the survival probability and obtain the exponential inequality for the ruin probability.
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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