两类Cox模型首达时与0点末离时的计算

The Computation of First Hitting Time and Last Exit Time of Zero Level for Two Different Cox Models

考虑了点过程为连续的Cox风险过程与点过程具有跳点的Cox风险过程,主要研究了这两类过程中的首达时和0点末离时的概率密度函数.对于第一种情况,通过建立经典过程的首达时与Cox过程首达时之间的关系,利用点过程的左连续逆的方法,给出了其L-S变换的显性表达.由于在第二种情况下,无法使用左连续逆的方法,直接对首达时的概率密度函数进行研究,通过概率的方法得到其表达式.进一步,通过类似方法,给出0点末离时的表达式.

The first hitting time and last exit time of zero level for two different Cox models are considered.For the continuous Cox process,the relationship between the hitting time of the Cox risk process and the classical risk processs is established,then an explicit expression of the Laplace-Stieltjes transform of the hitting time is derived by analyzing the left-continuous-inverse function of the point process.For Cox risk model with jump points,the Laplace-Stieltjes transform of the first hitting time is derived with the help of probability method.Further,through the similar analysis of the first hitting time,the expression of the probability density function of the last exit time of zero level is derived.