Limit theorems for certain functionals of unions of random closed sets
Teoriâ veroâtnostej i ee primeneniâ, Tome 47 (2002) no. 1, pp. 130-142
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Let $X_1,X_2,\dots$ be a sequence of independent identically distributed random closed subsets of a certain locally compact, Hausdorff, and separable space $E$. For each random closed set $Y$ we consider its avoidance functional $Q_Y(F)$ equal to the probability that $Y$ is disjoint with the closed subset $F\subseteq E$. The purpose of this paper is to establish limit theorems for the random variables $Q_Y(X_1\cup\dots\cup X_n)$. The results obtained are then applied for asymptotic analysis of the mean width of convex hulls generated by uniform samples on a multidimensional ball.
Keywords:
random sets, unions of closed sets, hitting functionals, extreme values, convex hulls, mean width, perimeter.
@article{TVP_2002_47_1_a8,
author = {T. Schreiber},
title = {Limit theorems for certain functionals of unions of random closed sets},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {130--142},
year = {2002},
volume = {47},
number = {1},
language = {en},
url = {http://geodesic.mathdoc.fr/item/TVP_2002_47_1_a8/}
}
T. Schreiber. Limit theorems for certain functionals of unions of random closed sets. Teoriâ veroâtnostej i ee primeneniâ, Tome 47 (2002) no. 1, pp. 130-142. http://geodesic.mathdoc.fr/item/TVP_2002_47_1_a8/