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

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 point where the drift is orthogonally projected.
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https://hal.archives-ouvertes.fr/hal-00880523
Contributor : Rodolphe Garbit <>
Submitted on : Sunday, August 17, 2014 - 7:29:47 PM
Last modification on : Monday, March 9, 2020 - 6:15:57 PM
Document(s) archivé(s) le : Thursday, November 27, 2014 - 1:56:38 AM

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Rodolphe Garbit, Kilian Raschel. On the exit time from a cone for Brownian motion with drift. Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2014, 19 (63), pp. 1-27. ⟨10.1214/EJP.v19-3169⟩. ⟨hal-00880523v2⟩

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