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Convergence in distribution of point processes on Polish spaces to a simple limit

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  • Peterson, Lisa D.
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    Abstract

    Let ξ,ξ1,ξ2,… be a sequence of point processes on a complete and separable metric space (S,d) with ξ simple. We assume that P{ξnB=0}→P{ξB=0} and lim supn→∞P{ξnB>1}≤P{ξB>1} for all B in some suitable class B, and show that this assumption determines if the sequence {ξn} converges in distribution to ξ. This is an extension to general Polish spaces of the weak convergence theory for point processes on locally compact Polish spaces found in Kallenberg (1996).

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 81 (2011)
    Issue (Month): 12 ()
    Pages: 1859-1861

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    Handle: RePEc:eee:stapro:v:81:y:2011:i:12:p:1859-1861

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    Related research

    Keywords: Convergence in distribution; Point processes; Simple point processes; Polish spaces;

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    1. Kallenberg, Olav, 1996. "Improved criteria for distributional convergence of point processes," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 64(1), pages 93-102, November.
    2. Elalaoui-Talibi, Hussain & Peterson, Lisa D., 2008. "Convergence in distribution of random compact sets in Polish spaces," Statistics & Probability Letters, Elsevier, Elsevier, vol. 78(6), pages 736-738, April.
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