Abstract
Let X̂ = C - Y where Y is a general one-dimensional Lévy process and C an independent subordinator. Consider the times when a new supremum of X̂ is reached by a jump of the subordinator C. We give a necessary and sufficient condition in order for such times to be discrete. When this is the case and X drifts to -oo, we decompose the absolute supremum of X̂ at these times, and derive a Pollaczek-Hinchin-type formula for the distribution function of the supremum.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 977-986 |
| Number of pages | 10 |
| Journal | Annales de l'institut Henri Poincare (B) Probability and Statistics |
| Volume | 44 |
| Issue number | 5 |
| DOIs | |
| State | Published - Oct 2008 |
Keywords
- Extrema
- Fluctuation theory
- Lévy process
- Risk theory
- Subordinator
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty