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A continuity theorem for cores of random closed sets
Author(s):
Pedro
Terán
Journal:
Proc. Amer. Math. Soc.
136
(2008),
4417-4425.
MSC (2000):
Primary 60D05
Posted:
July 18, 2008
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Abstract:
If a sequence of random closed sets  in a separable complete metric space converges in distribution in the Wijsman topology to  , then the corresponding sequence of cores (sets of probability measures dominated by the capacity functional of  ) converges to the core of the capacity of  . Core convergence is achieved not only in the Wijsman topology, but even in the stronger Vietoris topology. This is a generalization for unbounded random sets of the result proved by Artstein for random compact sets using the Hausdorff metric.
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Additional Information:
Pedro
Terán
Affiliation:
Facultad de Ciencias Económicas y Empresariales, Grupo Decisión Multicriterio Zaragoza, Universidad de Zaragoza, Gran Vía 2, E-50005 Zaragoza, Spain
Address at time of publication:
Miguel Servet 2, $2{}^\circ $D, E-33213, Gijón, Spain
Email:
teran@unizar.es
DOI:
10.1090/S0002-9939-08-09412-4
PII:
S 0002-9939(08)09412-4
Keywords:
Choquet capacity,
core,
random closed set,
Vietoris topology,
Wijsman topology
Received by editor(s):
December 29, 2006,
Received by editor(s) in revised form:
October 25, 2007
Posted:
July 18, 2008
Additional Notes:
This research was partially supported by Spain’s Ministerio de Educación y Ciencia under its research grants MTM2005-02254 and TSI2005-02511, and the Gobierno de Aragón under its research grant PM2004-052.
Communicated by:
Richard C. Bradley
Copyright of article:
Copyright
2008,
Pedro Ter\'an
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