By recursive method and Martingale method, we derive the integral equation for the survival probability and obtain the exponential inequality for the ruin probability.

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。

The differential and integral equation for survival probability and a upper bound of ruin probability are given by using renewal theory and stochastic process approach.

利用更新理论和随机过程等方法，给出了模型生存概率所满足的微积分方程关系式和破产概率的一个上界估计。

Large amplitude rolling motion and survival probability of biased ships are investigated using safe basin theory.

应用安全池思想研究随机海浪中倾斜船舶大幅横摇运动及倾覆概率问题.

Then we obtained the equations of the survival probability of two risk models with constant interest which have studied in chapter three by means of Laplace transform and change of the model.

然后将第三章的两个模型分别推广到带常利率情形，利用模型转换和拉普拉斯变换得到了生存概率满足的关系式。