RECTILINEAR AND BROWNIAN MOTION FROM A RANDOM POINT IN A CONVEX REGION
Abstract
A particle is projected from a point P in a subset E of a convex region H to a point Q in a uniformly random direction. The probability that Q lies in the interior of H at time t is obtained for two types of motion of the particle, rectilinear (i.e. straight-line) and Brownian. In the case of rectilinear motion, the first passage time through the boundary of H is considered. Results are obtained in terms of the generalized overlap function for embedded bodies.
Keywords
Brownian motion; convex body; geometric probability; random ray
DOI: 10.5566/ias.v20.p113-117
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