论文信息 - Limit Theorems for Certain Functionals of Unions of Random Closed Sets

Limit Theorems for Certain Functionals of Unions of Random Closed Sets

Let $X_{1},X_{2},\ldots$ 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 $Q_{Y}(X_{1} \cup \cdots \cup X_{n})$. The results obtained are then applied for asymptotic analysis of the mean width of convex hulls generated by uniform samples on a multidimensional ball.

T. Schreiber

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