Abstract
AbstractIn this paper, we obtain a Bernstein-type concentration inequality and McDiarmid’s inequality under upper probabilities for exponential independent random variables. Compared with the classical result, our inequalities are investigated under a family of probability measures, rather than one probability measure. As applications, the convergence rates of the law of large numbers and the Marcinkiewicz–Zygmund-type law of large numbers about the random variables in upper expectation spaces are obtained.
Funder
National Natural Science Foundation of China
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis
Reference26 articles.
1. Bercu, B., Delyon, B., Rio, E.: Concentration Inequalities for Sums and Martingales. Springer, New York (2015)
2. Bernstein, S.: Theory of Probability. Moscow (1927)
3. Chen, Z.: Strong laws of large numbers for capacities. Math. 46(15), 7529–7545 (2010)
4. Chen, Z.: Strong laws of large numbers for sub-linear expectations. Sci. China Math. 59(5), 945–954 (2016)
5. Chen, Z., Hu, F.: A law of the iterated logarithm under sublinear expectations. J. Financ. Eng. 1(02), 1450015 (2014)