RECTILINEAR AND BROWNIAN MOTION FROM A RANDOM POINT IN A CONVEX REGION

Peter Ehlers, Ernest Enns, Tak Fung

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

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DOI: 10.5566/ias.v20.p113-117

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Image Analysis & Stereology
EISSN 1854-5165 (Electronic version)
ISSN 1580-3139 (Printed version)