Institute of Information Theory and Automation

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Bibliography

Journal Article

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

Agahi H., Mohammadpour A., Mesiar Radko

: Brazilian Journal of Probability and Statistics vol.29, 4 (2015), p. 878-896

: Capacities, probability inequalities, Choquet-like expectation

: 10.1214/14-BJPS251

: http://library.utia.cas.cz/separaty/2019/E/mesiar-0506950.pdf

(eng): 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.

: BA

: 10103

2019-01-07 08:39