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

Lisa D. Peterson

Statistics & Probability Letters, 2011, vol. 81, issue 12, 1859-1861

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).

Keywords: Convergence in distribution; Point processes; Simple point processes; Polish spaces (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1016/j.spl.2011.07.018

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