Hitting Probabilities of Finite Points for One-Dimensional Lévy Processes
Abstract
For a one-dimensional Lévy process, we derive an explicit formula for the probability of first hitting a specified point among a fixed finite set. Moreover, using this formula, we obtain an explicit expression for each entry of the $Q$-matrix of the trace process on the finite set. These formulas involve solely the renormalized zero resolvent.
Fields of Study & Subjects
Stochastic processes and statistical mechanics
Probability and Statistical Research
Probability and Risk Models
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 10 February 2026
- Language
- EN
- Document type
- Preprint