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.

引用

页码：51 / 62

页数：12

共 42 条

[1] A Two-Sided First-Exit Problem for a Compound Poisson Process with a Random Upper Boundary
D. Perry
W. Stadje
S. Zacks
Methodology and Computing in Applied Probability, 2005, 7 : 51 - 62
[2] Number of Jumps in Two-Sided First-Exit Problems for a Compound Poisson Process
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Lu, Yi
Jin, Can
METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY, 2016, 18 (03) : 747 - 764
[3] Number of Jumps in Two-Sided First-Exit Problems for a Compound Poisson Process
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Can Jin
Methodology and Computing in Applied Probability, 2016, 18 : 747 - 764
[4] A two-sided exit problem for a difference of a compound poisson process and a compound renewal process with a discrete phase space
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[5] Upper first-exit times of compound poisson processes revisited
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[6] On the distribution of the first exit time and overshoot in a two-sided boundary crossing problem
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[7] Inverse first-exit problem for the Wiener process
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[8] On the upper first-exit times of compound G/M processes
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PROBABILITY IN THE ENGINEERING AND INFORMATIONAL SCIENCES, 2005, 19 (03) : 397 - 403
[9] Compound poisson processes with two-sided reflection
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Ukrainian Mathematical Journal, 2002, 54 (12) : 1958 - 1970
[10] Optimal Cash Management Problem for Compound Poisson Processes with Two-Sided Jumps
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APPLIED MATHEMATICS AND OPTIMIZATION, 2019, 80 (02): : 331 - 368

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