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Title
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On the Hausdorff measure of noncompactness for the parameterized Prokhorov metric
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Author
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Abstract
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| 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. |
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Language
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English
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Source (journal)
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Journal of Inequalities and Applications
Journal of inequalities and applications. - New York, N.Y.
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Publication
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SpringerOpen
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2016
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ISSN
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1029-242X
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DOI
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10.1186/S13660-016-1151-8
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Volume/pages
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(2016)
, 15 p.
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Article Reference
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215
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ISI
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000383027300002
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Medium
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E-only publicatie
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Full text (Publisher's DOI)
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Full text (open access)
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