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

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  • Peterson, Lisa D.

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).

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:12:p:1859-1861
    DOI: 10.1016/j.spl.2011.07.018
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    References listed on IDEAS

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    1. 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.
    2. Kallenberg, Olav, 1996. "Improved criteria for distributional convergence of point processes," Stochastic Processes and their Applications, Elsevier, vol. 64(1), pages 93-102, November.
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