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Generalizations of some probability inequalities and L-p convergence of random variables for any monotone measure
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SYSNO ASEP 0506950 Document Type J - Journal Article R&D Document Type The record was not marked in the RIV Subsidiary J Článek ve WOS Title Generalizations of some probability inequalities and L-p convergence of random variables for any monotone measure Author(s) Agahi, H. (IR)
Mohammadpour, A. (IR)
Mesiar, Radko (UTIA-B) RID, ORCIDNumber of authors 3 Source Title Brazilian Journal of Probability and Statistics - ISSN 0103-0752
Roč. 29, č. 4 (2015), s. 878-896Number of pages 19 s. Publication form Print - P Language eng - English Country BR - Brazil Keywords Capacities ; probability inequalities ; Choquet-like expectation Subject RIV BA - General Mathematics OECD category Statistics and probability Institutional support UTIA-B - RVO:67985556 UT WOS 000362310900009 EID SCOPUS 84941882338 DOI 10.1214/14-BJPS251 Annotation This paper has three specific aims. First, some probability inequal-ities, including Hölder’s inequality, Lyapunov’s inequality, Minkowski’s in-equality, concentration inequalities and Fatou’s lemma for Choquet-like ex-pectation based on a monotone measure are shown, extending previous workof many researchers. Second, we generalize some theorems about the con-vergence of sequences of random variables on monotone measure spaces forChoquet-like expectation. Third, we extend the concept of uniform integra-bility for Choquet-like expectation. These results are useful for the solutionof various problems in machine learning and made it possible to derive newefficient algorithms in any monotone system. Corresponding results are validfor capacities, the usefulness of which has been demonstrated by the rapidlyexpanding literature on generalized probability theory. Workplace Institute of Information Theory and Automation Contact Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201. Year of Publishing 2020
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