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

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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Year of publication:	2011
Authors:	Peterson, Lisa D.
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 81.2011, 12, p. 1859-1861
Publisher:	Elsevier
Subject:	Convergence in distribution \| Point processes \| Simple point processes \| Polish spaces

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10011040146