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

Autor(en): Kella, O
Stadje, W 
Stichwörter: confluent hypergeometric functions; dam with linear release rates; hitting times; Markov process; Mathematics; shot-noise process; Statistics & Probability
Erscheinungsdatum: 2001
Herausgeber: APPLIED PROBABILITY TRUST
Journal: JOURNAL OF APPLIED PROBABILITY
Volumen: 38
Ausgabe: 3
Startseite: 781
Seitenende: 786
Zusammenfassung: 
For a compound Poisson dam with exponential jumps and linear release rate (shot-noise process), we compute the Laplace-Stieltjes transform (LST) and the mean of the hitting time of some positive level given that the process starts 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).
ISSN: 00219002
DOI: 10.1017/S0021900200018945

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