半正定(半负定)二元函数基于g-期望的Jensen不等式

Jensen′s Inequality for g-expectation on Semi-positive Definite(Semi-negative Definite) Bivariate Function

彭实戈通过倒向随机微分方程引入了g-期望的概念.在关于g-期望的最基本的条件下,提出并证明了:半正定(半负定)二元函数基于g-期望的Jensen不等式在非空数集S上成立当且仅当生成元g在S上是超线性(次线性)的.

Peng S G. introduced the notion of g-expectation by backward stochastic differential equation. Under the most elementary conditions with respect to g-expectation, this paper puts forword and proves that Jensen＇s inequality for g-expectation on semi-positive definite （resp. semi-negatlve definite） bivariate function holds on nonempty real sets S if and only if the generator g is super-linear （resp. sub-linear） on S.