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Convergence in distribution of random compact sets in Polish spaces

Author

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  • Elalaoui-Talibi, Hussain
  • Peterson, Lisa D.

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.]

Suggested Citation

  • Elalaoui-Talibi, Hussain & Peterson, Lisa D., 2008. "Convergence in distribution of random compact sets in Polish spaces," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 736-738, April.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:6:p:736-738
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    Cited by:

    1. Peterson, Lisa D., 2011. "Convergence in distribution of point processes on Polish spaces to a simple limit," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1859-1861.

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