On hitting times for compound Poisson dams with exponential jumps and linear release rate

Authors
Kella, O Stadje, W
Citation
O. Kella et W. Stadje, On hitting times for compound Poisson dams with exponential jumps and linear release rate, J APPL PROB, 38(3), 2001, pp. 781-786
Citations number
7
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF APPLIED PROBABILITY
ISSN journal
00219002 → ACNP
Volume
38
Issue
3
Year of publication
2001
Pages
781 - 786
Database
ISI
SICI code
0021-9002(200109)38:3<781:OHTFCP>2.0.ZU;2-7
Abstract
For a compound Poisson dam with exponential jumps and linear release rate ( shot-noise process), we compute the Laplace-Stieltjes transform (LST) and t he mean of the hitting time of some positive level given that the process s tarts from some given positive level. The solution for the LST is in terms of confluent hypergeometric functions of the first and second kinds (Kummer functions).