Computation of the first-order moment measure of a random process of segments on the two dimensional Euclidean sphere. (English. Russian original) Zbl 0749.60008

Petunin, Yu. I.; Semejko, N. G.

Theory Probab. Math. Stat. 42, 137-144 (1991); translation from Teor. Veroyatn. Mat. Stat., Kiev 42, 114-122 (1990).

In continuation of earlier investigations [ibid. 39, 129-135 (1989), resp. ibid. 39, 107-113 (1988; Zbl 0665.60019) and ibid. 41, 105-113 (1990), resp. ibid. 41, 88-96 (1989; Zbl 0696.60016)], the authors consider a point process \(X\) of segments on the two-dimensional unit sphere \(S^ 2\). Here, a ‘segment’ means a spherical cap and \(X\) is assumed to result from a rotation invariant center process (with finite intensity) with independently chosen cap diameters (a marked point process). For a given trapezoid \(R\subset S^ 2\), the authors calculate the mean number of caps (in \(X\)) intersecting \(R\).

Reviewer: W.Weil (Karlsruhe)

MSC:

60D05	Geometric probability and stochastic geometry
60G55	Point processes (e.g., Poisson, Cox, Hawkes processes)

Keywords:

random caps; principal kinematic formula on the sphere; trapezoid; mean number of caps

Citations:

Zbl 0713.60017; Zbl 0709.60010; Zbl 0665.60019; Zbl 0696.60016