A two-sided first-exit problem for a compound poisson process with a random upper boundary
| Autor(en): | Perry, D Stadje, W Zacks, S |
Stichwörter: | compound Poisson process; COUNTING-PROCESSES; first-exit time; integral equation; linear boundary; M/G/1; Mathematics; QUEUES; random boundary; Statistics & Probability; TIMES | Erscheinungsdatum: | 2005 | Herausgeber: | SPRINGER | Journal: | METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY | Volumen: | 7 | Ausgabe: | 1 | Startseite: | 51 | Seitenende: | 62 | Zusammenfassung: | 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. |
ISSN: | 13875841 | DOI: | 10.1007/s11009-005-6654-6 |
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