次线性期望下随机加权END序列的完全积分收敛

Complete Integral Convergence of Randomly Weighted END Sequence Under Sub-Linear Expectation

次线性期望下的极限理论具有挑战性,并且引起了人们的广泛关注和探索。运用不同于概率空间的研究方法,在Choquet积分存在的条件下,利用Holder不等式和广义负相依(END)序列的容度不等式,研究次线性期望下随机加权END随机变量序列的完全积分收敛性,得到了完全收敛和完全积分收敛定理,从而把该定理从传统概率空间拓展到次线性期望空间。此外,定理的结果也对次线性期望下的一些结果进行了推广。

Limit theory under sub-linear expectation is challenging and has attracted a great deal of attention and exploration.Adopt the different approach than probability space,under the condition that Choquet integrals existed,we used Holder inequality and extended negatively dependent(END)capacities inequality to study the complete integral convergence for randomly weighted END random variables sequence under the sub-linear expectation,and obtained the theorems of complete convergence and complete integral convergence,thereby extending the corresponding results from the probability space to the sub-linear expectations space.Moreover,the results extend some corresponding ones under sub-linear expectations.