Convergence *of* probabilities - Article 100 - go-pugleaf

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Convergence of probabilities

#100

From: ALEWAND
Date: Tue, 28 Jul 1992 10:39

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Let X1,X2,.. be a sequence of k-dimensional random vectors
converging in distribution to a random vector X.
Let A1,A2,.. be any sequence of k-dim. closed spheres.
Does anybody know sufficient conditions to show
       Pn(Xn in An)=P(X in An) + o(1)?
Remark: the usual theorems state only
       Pn(Xn in A)=P(X in A) + o(1) for all P-continuity sets A.
In particular what happens if X is N(0,F) with singular F?
 
Thanks in advance!
 
Achim Lewandowski
Institut fuer Statistik und Oekonometrie
3400 Goettingen
Germany
email: alewand@ibm.gwdg.de

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From: ALEWAND@ibm.gwdg.de
Subject: Convergence *of* probabilities
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Date: Tue, 28 Jul 92 10:39:41 MSZ
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