First passage time of filtered Poisson process with exponential shape function

被引：14
|
作者：
Novikov, A
Melchers, RE
Shinjikashvili, E
Kordzakhia, N
机构：
[1] Univ Technol Sydney, Dept Math Sci, Sydney, NSW 2007, Australia
[2] Univ Newcastle, Dept Civil Engn, Newcastle, NSW 2308, Australia
[3] Commonwealth Bank Australia, Quantitat Anal Risk Management, Sydney, NSW 1155, Australia
来源：
PROBABILISTIC ENGINEERING MECHANICS | 2005年 / 20卷 / 01期
基金：
澳大利亚研究理事会;
关键词：
first passage times; laplace transform; martingales; integro-differential equations; filtered Poisson process; Omstein-Uhlenbeck process;
D O I：
10.1016/j.probengmech.2004.04.005
中图分类号：
TH [机械、仪表工业];
学科分类号：
0802 ;
摘要：
Solving some integro-differential equation we find the Laplace transform of the first passage time for filtered Poisson process generated by pulses with uniform or exponential distributions. Also, the martingale technique is applied for approximations of expectations and distributions of the first passage times. The approximations accuracy is verified with the help of Monte-Carlo simulations. (C) 2004 Elsevier Ltd. All rights reserved.
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页码：57 / 65
页数：9
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