Title
On the Hausdorff measure of noncompactness for the parameterized Prokhorov metricOn the Hausdorff measure of noncompactness for the parameterized Prokhorov metric
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Research group
Fundamental Mathematics
Publication type
article
Publication
New York, N.Y.,
Subject
Mathematics
Source (journal)
Journal of inequalities and applications. - New York, N.Y.
Volume/pages
(2016), 15 p.
ISSN
1025-5834
1029-242X
Article Reference
215
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
We quantify the Prokhorov theorem by establishing an explicit formula for the Hausdorff measure of noncompactness (HMNC) for the parameterized Prokhorov metric on the set of Borel probability measures on a Polish space. Furthermore, we quantify the Arzelà-Ascoli theorem by obtaining upper and lower estimates for the HMNC for the uniform norm on the space of continuous maps of a compact interval into Euclidean N-space, using Jungs theorem on the Chebyshev radius. Finally, we combine the obtained results to quantify the stochastic Arzelà-Ascoli theorem by providing upper and lower estimates for the HMNC for the parameterized Prokhorov metric on the set of multivariate continuous stochastic processes.
Full text (open access)
https://repository.uantwerpen.be/docman/irua/d79735/135211.pdf
https://repository.uantwerpen.be/docman/irua/03cd72/135211.pdf
Handle