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

Authors

  • Peter Ehlers
  • Ernest Enns
  • Tak Fung

DOI:

https://doi.org/10.5566/ias.v20.p113-117

Keywords:

Brownian motion, convex body, geometric probability, random ray

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.

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Published

2011-05-03

Issue

Section

Original Research Paper

How to Cite

Ehlers, P., Enns, E., & Fung, T. (2011). RECTILINEAR AND BROWNIAN MOTION FROM A RANDOM POINT IN A CONVEX REGION. Image Analysis and Stereology, 20(2), 113-117. https://doi.org/10.5566/ias.v20.p113-117

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