First exit from an open set for a matrix-exponential Lévy process

Yu Ting Chen*, Yu Tzu Chen, Yuan-Chung Sheu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We study the first exit from a general open set for a one-dimensional Lévy process, where the Lévy measure is proportional to a two-sided matrix-exponential distribution. Under appropriate conditions on the Lévy measure, we obtain an explicit solution for the joint distribution of the first-exit time and the position of the Lévy process upon first exit, in terms of the zeros and poles of the corresponding Laplace exponent. The present result complements several earlier works on the use of exit sets for Lévy processes with algebraically similar Laplace exponents, where exits from open intervals are the main focus.

Original languageEnglish
Pages (from-to)104-110
Number of pages7
JournalStatistics and Probability Letters
StatePublished - 1 Aug 2017


  • First exit problems
  • Jump diffusions
  • Lévy processes
  • Matrix-exponential distributions

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