Convergence in distribution of random compact sets in Polish spaces

Hussain Elalaoui-Talibi and Lisa D. Peterson

Statistics & Probability Letters, 2008, vol. 78, issue 6, 736-738

Abstract: Let [phi],[phi]1,[phi]2,... be a sequence of random compact sets on a complete and separable metric space (S,d). We assume that P{[phi]n[intersection]B=[empty set]}-->P{[phi][intersection]B=[empty set]} for all B in some suitable class and show that this assumption determines if the sequence {[phi]n} converges in distribution to [phi]. This is an extension to general Polish spaces of the weak convergence theory for random closed sets on locally compact Polish spaces found in Norberg [1984. Convergence and existence of random set distributions. Ann. Probab. 12, 726-732.]

Keywords: Convergence; in; distribution; Random; compact; sets; Polish; spaces (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (1)

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