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Random cap processes and generalized Wicksell problem on the surface of a sphere. (English) Zbl 0770.60009
Summary: The properties of the random process of the closed hemispherical caps on the surface of a two-dimensional Euclidean sphere are investigated by using the theory of marked point processes. A first order moment measure of the marked point process of the parameters corresponding to the cap process is found. This measure permits to calculate the first order moment measure of the cap process for the spherical sets of the special forms. The properties of the random chord process on the big circle of the sphere induced by the cap process are investigated. The first order moment measure of the chord process is obtained. The well-known Wicksell problem is generalized for the surface of a two-dimensional Euclidean sphere.
MSC:
60D05 Geometric probability and stochastic geometry
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
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