RECTILINEAR AND BROWNIAN MOTION FROM A RANDOM POINT IN A CONVEX REGION
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 rectil...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Slovenian Society for Stereology and Quantitative Image Analysis
2011-05-01
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| Series: | Image Analysis and Stereology |
| Subjects: | |
| Online Access: | http://www.ias-iss.org/ojs/IAS/article/view/665 |
| Summary: | 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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| ISSN: | 1580-3139 1854-5165 |