Turkish Journal of Mathematics
DOI
10.3906/mat-1705-106
Abstract
In the definition of weak convergence of probability measures it is assumed that the limit is a probability measure as well. We get rid of this assumption and require that the limit merely needs to be a Choquet-capacity functional. In terms of random variables this means that the distributional limit no longer is a random point, but a random closed set, namely one uniquely determined by the Choquet capacity. For our extended notion of weak convergence there is a counterpart of the portmanteau theorem. Moreover, we demonstrate basic relations to the theory of random closed sets with emphasis on weak convergence in hyperspace topologies including two correspondence theorems. Finally, the approach carries over to sequences of Choquet capacities.
Keywords
Weak convergence, Choquet capacity, Fell topology, upper Vietoris topology, random closed set
First Page
1747
Last Page
1764
Recommended Citation
FERGER, DIETMAR
(2018)
"Weak convergence of probability measures to Choquet capacity functionals,"
Turkish Journal of Mathematics: Vol. 42:
No.
4, Article 16.
https://doi.org/10.3906/mat-1705-106
Available at:
https://journals.tubitak.gov.tr/math/vol42/iss4/16
