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

Offer Kella*, Wolfgang Stadje

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

22 Scopus citations

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 languageAmerican English
Pages (from-to)781-786
Number of pages6
JournalJournal of Applied Probability
Volume38
Issue number3
DOIs
StatePublished - Sep 2001

Keywords

  • Confluent hypergeometric functions
  • Dam with linear release rates
  • Hitting times
  • Markov process
  • Shot-noise process

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