中文摘要：

在倒向随机微分方程生成元满足基本假设的前提下,通过次线性g-期望所控制的一族概率测度,得到了受控于该次线性g-期望的凸g-期望的一个新的表示.进一步地,对任意给定的凸g-期望,证明了控制该凸g-期望的极小次线性g-期望的存在性.

英文摘要：

Under the basic assumptions on generators that for any convex g-expectation dominated by some sublinear g-expectation,there exists a set of probability measures controlled by the sublinear g-expectation,a new representation of these convex g-expectations has been obtained in this work. Furthermore,for any given convex gexpectation,we show the existence of the minimal sublinear g-expectations dominating the convex g-expectation from above.