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 est...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 sublinear expectation for random variables with only finite variances.展开更多
We prove a new Donsker’s invariance principle for independent and identically distributed random variables under the sub-linear expectation.As applications,the small deviations and Chung’s law of the iterated logari...We prove a new Donsker’s invariance principle for independent and identically distributed random variables under the sub-linear expectation.As applications,the small deviations and Chung’s law of the iterated logarithm are obtained.展开更多
基金supported by National Natural Science Foundation of China (Grant No. 11225104)the National Basic Research Program of China (Grant No. 2015CB352302)the Fundamental Research Funds for the Central Universities
文摘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 sublinear expectation for random variables with only finite variances.
基金This research supported by Grants from the National Natural Science Foundation of China(No.11225104)and the Fundamental Research Funds for the Central Universities.
文摘We prove a new Donsker’s invariance principle for independent and identically distributed random variables under the sub-linear expectation.As applications,the small deviations and Chung’s law of the iterated logarithm are obtained.
