Rosenthal’s inequalities for independent and negatively dependent random variables under sub-linear expectations with applications
By Li-Xin Zhang. 2014
189 citations recorded by the source corpus.
Classical Kolmogorov’s and Rosenthal’s inequalities for the maximum partial sums of random variables are basic tools for studying the strong laws of large numbers. In this paper, motived by the notion of independent and identically distributed random variables under the sub-linear expectation initiated by Peng (2008), we introduce the concept of negative dependence of random variables and establish Kolmogorov’s and Rosenthal’s inequalities for the maximum partial sums of negatively dependent random variables under the sub-linear expectations. As an application, we show that Kolmogorov’s strong law of larger numbers holds for independent and identically distributed random variables under a continuous sub-linear expectation if and only if the corresponding Choquet integral is finite.
Subfields: Demography, Finance, Management Science and Operations Research
View Paper: https://www.semanticscholar.org/paper/f29e1cb786701aa698abde8bd756e725434a52b6
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Citations in the corpus
- Exponential inequalities under the sub-linear expectations with applications to laws of the iterated logarithm (2014, methodology): “We also need the Rosenthal type inequalities under Ê which have been obtained by Zhang (2014).”
- Donsker’s Invariance Principle Under the Sub-linear Expectation with an Application to Chung’s Law of the Iterated Logarithm (2015, methodology): “The condition was relaxed to only the existence of the second moments by Zhang (2014b).”
- Strong limit theorems for extended independent and extended negatively dependent random variables under non-linear expectations (2016, background): “For proving the theorems, we need the following lemma which can be found in Zhang (2016).”