Generalizations of some probability inequalities and L-p convergence of random variables for any monotone measure

0506950 - ÚTIA 2020 BR eng J - Journal Article
Agahi, H. - Mohammadpour, A. - Mesiar, Radko
Generalizations of some probability inequalities and L-p convergence of random variables for any monotone measure.
Brazilian Journal of Probability and Statistics. Roč. 29, č. 4 (2015), s. 878-896. ISSN 0103-0752. E-ISSN 0103-0752
Institutional support: RVO:67985556
Keywords : Capacities * probability inequalities * Choquet-like expectation
OECD category: Statistics and probability
Impact factor: 0.420, year: 2015
http://library.utia.cas.cz/separaty/2019/E/mesiar-0506950.pdf

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.
Permanent Link: http://hdl.handle.net/11104/0298083