On hitting times for compound Poisson dams with exponential jumps and linear release rate
Offer Kella and Wolfgang Stadje
Source: J. Appl. Probab. Volume 38, Number 3
(2001), 781-786.
Abstract
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).
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Keywords: Dam with linear release rates; shot-noise process; Markov process; hitting times; confluent hypergeometric functions
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jap/1005091042
Digital Object Identifier: doi:10.1239/jap/1005091042
Mathematical Reviews number (MathSciNet): MR1860216
Zentralblatt MATH identifier: 0994.60092
Journal of Applied Probability
