Electronic Journal of Probability

On the exit time from a cone for brownian motion with drift

Rodolphe Garbit and Kilian Raschel

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Abstract

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.

Article information

Source
Electron. J. Probab., Volume 19 (2014), paper no. 63, 27 pp.

Dates
Accepted: 20 July 2014
First available in Project Euclid: 4 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465065705

Digital Object Identifier
doi:10.1214/EJP.v19-3169

Mathematical Reviews number (MathSciNet)
MR3238783

Zentralblatt MATH identifier
1317.60104

Subjects
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]

Keywords
Brownian motion with drift Exit time Cone Heat kernel

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

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


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