On the asymptotic approximation of inverse moment under sub-linear expectations

Precise Asymptotics for Complete Integral Convergence under Sublinear Expectations

“…A series of useful results have been established. Peng [1,7,8] constructed the basic framework, basic properties, and central limit theorem under sublinear expectations, Zhang [9][10][11] established the exponential inequalities, Rosenthal's inequalities, strong law of large numbers, and law of iterated logarithm, Hu [12], Chen [13], and Wu and Jiang [14] studied strong law of large numbers, Wu et al [15] studied the asymptotic approximation of inverse moment, Xi et al [16] and Lin and Feng [17] studied complete convergence, and so on. In general, extending the limit properties of conventional probability space to the cases of sublinear expectation is highly desirable and of considerably significance in the theory and application.…”

Exponential inequalities under sub-linear expectations with applications to strong law of large numbers

“…Zhang [9]). In addition, Chen [10] investigated kinds of strong laws of large numbers for capacities, Zhang [11] obtained the moment inequalities and the Kolmogorov type exponential inequalities, Wu and Chen [12] researched the invariance principles for the law of the iterated logarithm, Wu and Jiang [13] established the strong law of large numbers and Chover's law of the iterated logarithm under sub-linear expectations, Wu et al [14] investigated the approximations of inverse moments for double-indexed weighted sums of random variables and obtained the convergence rate of approximations under sub-linear expectations, and so on. In this work, we will further study the probability limit properties for partial sums of random variables under the sub-linear expectations, especially the exponential inequalities for unbounded random variables and applications to the convergence rate of the strong law of large numbers.…”