Electronic Journal of Probability
- Electron. J. Probab.
- Volume 19 (2014), paper no. 63, 27 pp.
On the exit time from a cone for brownian motion with drift
We investigate the tail distribution of the first exit time of Brownian motion with drift from a cone and find its exact asymptotics for a large class of cones. Our results show in particular that its exponential decreasing rate is a function of the distance between the drift and the cone, whereas the polynomial part in the asymptotics depends on the position of the drift with respect to the cone and its polar cone, and reflects the local geometry of the cone at the points that minimize the distance to the drift.
Electron. J. Probab., Volume 19 (2014), paper no. 63, 27 pp.
Accepted: 20 July 2014
First available in Project Euclid: 4 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60F17: Functional limit theorems; invariance principles
Secondary: 60G50: Sums of independent random variables; random walks 60J05: Discrete-time Markov processes on general state spaces 60J65: Brownian motion [See also 58J65]
This work is licensed under a Creative Commons Attribution 3.0 License.
Garbit, Rodolphe; Raschel, Kilian. On the exit time from a cone for brownian motion with drift. Electron. J. Probab. 19 (2014), paper no. 63, 27 pp. doi:10.1214/EJP.v19-3169. https://projecteuclid.org/euclid.ejp/1465065705