Publication
Title
On the Hausdorff measure of noncompactness for the parameterized Prokhorov metric
Author
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.
Language
English
Source (journal)
Journal of inequalities and applications. - New York, N.Y.
Publication
New York, N.Y. : 2016
ISSN
1025-5834
Volume/pages
(2016), 15 p.
Article Reference
215
ISI
000383027300002
Medium
E-only publicatie
Full text (Publisher's DOI)
Full text (open access)
UAntwerpen
Faculty/Department
Research group
Publication type
Subject
Affiliation
Publications with a UAntwerp address
External links
Web of Science
Record
Identification
Creation 12.09.2016
Last edited 14.09.2017
To cite this reference