Concentration inequalities for upper probabilities

[摘要] In 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.

[学科分类] 电力

[关键词] Concentration inequality;Law of large numbers;Upper probability;Sublinear expectation