A two-sided first-exit problem for a compound poisson process with a random upper boundary

被引：17
|
作者：
Perry, D [1 ]
Stadje, W
Zacks, S
机构：
[1] Univ Haifa, Dept Stat, IL-31905 Haifa, Israel
[2] Univ Osnabruck, Dept Math & Comp Sci, D-49069 Osnabruck, Germany
[3] SUNY Binghamton, Dept Math Sci, Binghamton, NY 13902 USA
来源：
METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY | 2005年 / 7卷 / 01期
关键词：
compound Poisson process; linear boundary; random boundary; first-exit time; integral equation;
D O I：
10.1007/s11009-005-6654-6
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
We consider the first-exit time of a compound Poisson process from a region that is bounded from below by an increasing straight line, while its upper boundary has positive jumps of i.i.d. sizes at Poisson times and increases linearly between jumps. An integral equation for the corresponding Laplace-Stieltjes transforms is derived and solved. The case of exponential jumps is treated separately. The problem has applications in queueing and risk theory.
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页码：51 / 62
页数：12
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