Strong law of large numbers and Chover's law of the iterated logarithm under sub-linear expectations

On Some Conditions for Strong Law of Large Numbers for Weighted Sums of END Random Variables under Sublinear Expectations

“…For example, Zhang [7][8][9] acquired the exponential inequalities, Rosenthal's inequalities, Kolmogorovs strong law of larger numbers (SLLNs) and Hartman-Wintners law of iterated logarithm, Yu and Wu [10] obtained complete convergence for weighted sums of extended negatively dependent random variables under a specific moment condition, Cheng [11] established strong law of large numbers (SLLNs) under a general moment condition and so on. And many strong laws of large numbers for weighted sums of some sequences have been obtained; one can refer to Chen [12], Wu and Jiang [13], Zhang [14], Chen et al [15], and Chen and Liu [16]. These authors only researched Kolmogorov's SLLNs or Marcinkiewicz's SLLNs for some sequences of random variables.…”

Precise Asymptotics in the Law of the Iterated Logarithm under Sublinear Expectations

“…Yu and Wu [8] studied Marcinkiewicz-type complete convergence for weighted sums under sublinear expectations. Wu and Jiang [9] obtained a strong law of large numbers and Chover's law of the iterated logarithm under sublinear expectations. Ma and Wu [10] studied the limiting behavior of weighted sums of extended negatively dependent random variables under sublinear 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.…”