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

D. Perry; Wolfgang Stadje; Shelly Zacks

doi:10.1007/s11009-005-6654-6

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

D. Perry, Wolfgang Stadje, Shelly Zacks

Department of Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	51-62
Number of pages	12
Journal	Methodology and Computing in Applied Probability
Volume	7
Issue number	1
DOIs	https://doi.org/10.1007/s11009-005-6654-6
State	Published - Mar 2005

Keywords

Compound Poisson process
First-exit time
Integral equation
Linear boundary
Random boundary

ASJC Scopus subject areas

Statistics and Probability
General Mathematics

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10.1007/s11009-005-6654-6

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KW - Integral equation

KW - Linear boundary

KW - Random boundary

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

Abstract

Keywords

ASJC Scopus subject areas

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