First passage time density of an Ornstein–Uhlenbeck process with broken drift.
- Resource Type
- Article
- Authors
- Ankirchner, Stefan; Blanchet-Scalliet, Christophette; Dorobantu, Diana; Gay, Laura
- Source
- Stochastic Models. 2022, Vol. 38 Issue 2, p308-329. 22p.
- Subject
- *ORNSTEIN-Uhlenbeck process
*DISTRIBUTION (Probability theory)
*DENSITY
*FOKKER-Planck equation
- Language
- ISSN
- 1532-6349
We consider an Ornstein–Uhlenbeck process with different drift rates below and above zero. We derive an analytic expression for the density of the first time, where the process hits a given level. The passage time density is linked to the joint law of the process and its running supremum, and we also provide an analytic formula of the joint density/distribution function. Results from a numerical experiment reveal that our formulas allow to numerically evaluate the joint law and the density of the first passage time faster than a simulation-based method. [ABSTRACT FROM AUTHOR]