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).
| Original language | English |
|---|---|
| Pages (from-to) | 781-786 |
| Number of pages | 6 |
| Journal | Journal of Applied Probability |
| Volume | 38 |
| Issue number | 3 |
| DOIs | |
| State | Published - Sep 2001 |
Keywords
- Confluent hypergeometric functions
- Dam with linear release rates
- Hitting times
- Markov process
- Shot-noise process