基于g期望的Minkowski不等式

Minkowski inequality for g expectation

为了证明g期望的Minkowski不等式,在g满足次线性条件下,针对非负生成元,利用比较定理和Young不等式,介绍了g期望的Hlder不等式;然后借助于该不等式证明了对于任意平方可积随机变量,当g满足次线性条件且为正值生成元时,g期望的Minkowski不等式成立。

To prove Minkowski inequality for g expectation, this paper is concerned with the use of the well-known comparison theorem and Young inequality for the introduction of the Holder inequality for g expectation when g satisfies the sublinear condition and is a nonnegative generator and the paper features the use of this inequality to prove that, for any square integrable random variables, Minkowski inequality for g expectation is valid when g is a positive-value sublinear generator.