一类复合泊松过程的首达时概率密度  

On the First Passage Time Density for a Class of Compound Poisson Process

作　　者：陶秀丽 沈兆晖 TAO Xiuli;SHEN Zhaohui(School of Mathematics and Statistics,Wuhan University,Wuhan 430072,Hubei,China)

机构地区：[1]武汉大学数学与统计学院,湖北武汉430072

出　　处：《武汉大学学报（理学版）》2021年第3期256-262,共7页Journal of Wuhan University:Natural Science Edition

摘　　要：利用复合泊松过程的独立增量性,研究了一类带正跳跃的复合泊松过程首达时的概率密度函数,这类复合泊松过程的跳跃幅度服从有限离散分布。由首达时的概率密度函数,计算出首达时有限的概率。而后,作为主要结论的应用,计算了几个特殊例子,推广了关于独立泊松过程的加权和过程的首达时概率分布的一些结论。Using the independent increment property of compound Poisson process,we studied the probability density function of the first passage time of a class of compound Poisson processes with positive jumps.The jump size of those compound Poisson processes satisfies finite discrete distribution.From the probability density function of the first passage time,we derived the probability of which first passage time is finite.Then,as the applications of the main results of this article,several special cases were discussed,and some results about the probability distribution of the first passage time of weighted Poisson processes were generalized.

关 键 词：复合泊松过程 首达时 概率密度函数 

分 类 号：O211.62[理学—概率论与数理统计]