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.
Rodolphe Garbit. Kilian Raschel. "On the exit time from a cone for brownian motion with drift." Electron. J. Probab. 19 1 - 27, 2014. https://doi.org/10.1214/EJP.v19-3169