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

Abstract

By an inequality of partial sum and uniform convergence of the central limit theorem under sublinear expectations, we establish precise asymptotics in the law of the iterated logarithm for independent and identically distributed random variables under sublinear expectations.

Equivalent Conditions of Complete p th Moment Convergence for Weighted Sums of I. I. D. Random Variables under Sublinear Expectations

“…Wu [6] obtained precise asymptotics for complete integral convergence. Xu and Cheng [7] studied precise asymptotics in the law of iterated logarithm under sublinear expectations.…”

Limiting behaviour of moving average processes genenrated by negatively dependent random variables under sub-linear expectations

“…[Gao and Xu(2011)], [Kuczmaszewska(2020)], [Xu and Cheng(2021c), Xu and Cheng(2021b), Xu and Cheng(2021a), Xu and Cheng(2022a), Xu and Cheng(2022b)] and references therein.…”

Convergence for sums of i.i.d. random variables under sublinear expectations

“…Inspired by the works of Zhang [12][13][14][15], Huang and Wu [5] and Zhong and Wu [16] studied some limits theorems under sublinear expectation space. Recently, under sublinear expectations, Wu [10] proved precise asymptotics for complete integral convergence, and Xu and Cheng [11] established precise asymptotics in the law of iterated logarithm. Under sublinear expectations for more limit theorems, the interested reader can refer to Chen [1], Xu [2], Hu et al [3], Hu and Yang [4], and references therein.…”