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Plate and line segment processes

Published online by Cambridge University Press:  14 July 2016

N. A. Fava  and
L. A. Santaló
N. A. Fava
Affiliation:
University of Buenos Aires
L. A. Santaló
Affiliation:
University of Buenos Aires
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Abstract

Random processes of convex plates and line segments imbedded in R3 are considered in this paper, and the expected values of certain random variables associated with such processes are computed under a mean stationarity assumption, by resorting to some general formulas of integral geometry.

Keywords

GEOMETRICAL PROBABILITYINTEGRAL GEOMETRYRANDOM SETSCONVEX PLATESLINE SEGMENTSPOISSON DISTRIBUTION
Type
Research Papers
Information
Journal of Applied Probability , Volume 15 , Issue 3 , September 1978 , pp. 494 - 501
Copyright
Copyright © Applied Probability Trust 1978 

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References

[1] Berman, M. (1977) Distance distributions associated with Poisson processes of geometric figures. J. Appl. Prob. 14, 195–199.CrossRefGoogle Scholar
[2] Coleman, R. (1974) The distance from a given point to the nearest end of one member of a random process of linear segments. In Stochastic Geometry, ed. Harding, E. F. and Kendall, D. G., Wiley, New York, 192–201.Google Scholar
[3] Parker, P. and Cowan, R. (1976) Some properties of line segment processes. J. Appl. Prob. 13, 96–107.CrossRefGoogle Scholar
[4] Santaló, L. A. (1936) Integralgeometrie 5. Exposés de Géométrie, Hermann et Cie, Paris.Google Scholar
[5] Santaló, L. A. (1976) Integral geometry and geometric probability. In Encyclopedia of Mathematics and its Applications. Addison Wesley, London.Google Scholar