Exponential inequalities under the sub-linear expectations with applications to laws of the iterated logarithm
By Li-Xin Zhang. 2014
143 citations recorded by the source corpus.
Kolmogorov’s exponential inequalities are basic tools for studying the strong limit theorems such as the classical laws of the iterated logarithm for both independent and dependent random variables. This paper establishes the Kolmogorov type exponential inequalities of the partial sums of independent random variables as well as negatively dependent random variables under the sub-linear expectations. As applications of the exponential inequalities, the laws of the iterated logarithm in the sense of non-additive capacities are proved for independent or negatively dependent identically distributed random variables with finite second order moments. For deriving a lower bound of an exponential inequality, a central limit theorem is also proved under the sub-linear expectation for random variables with only finite variances.
Subfields: Management Science and Operations Research, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/a52049596b1578cabd33e5d710bcd42db5d23696
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Management Science and Operations Research
In Statistics and Probability
Citations in the corpus
- Strong limit theorems for extended independent and extended negatively dependent random variables under non-linear expectations (2016, background): “…theorem and weak law of large numbers (cf. Peng (2008b, 2010)), the law of the iterated algorithm (cf. Chen and Hu (2014), Zhang (2015a)), the small derivation and Chung’s law of the iterated logarithm (c.f. Zhang (2015b)), the moment inequalities for the maximum partial sums (cf., Zhang (2016)).”
- 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).”