Characterization of random closed sets stable with respect to union. (English. Russian original) Zbl 0839.60016

Molchanov, I. S.

Theory Probab. Math. Stat. 46, 111-116 (1993); translation from Teor. Jmovirn. Mat. Stat. 46, 114-120 (1992).

This paper gives necessary and sufficient conditions for a random closed set in a Euclidean space to be union-stable. These conditions are expressed in terms of the Choquet capacity functional characterizing the distributions of random closed sets. The obtained results generalize earlier similar characterizations for random closed sets having no fixed points as can be found in G. Matheron’s famous book “Random sets and integral geometry” (1975; Zbl 0321.60009).

Reviewer: L.Heinrich (Freiberg)

MSC:

60D05	Geometric probability and stochastic geometry
60E07	Infinitely divisible distributions; stable distributions

Keywords:

union-infinitely divisible; random closed set; Choquet capacity

Citations:

Zbl 0321.60009