非线性数学期望的收敛定理  

Convergent Theorems for Nonlinear Mathematical Expectation

作　　者：范胜君[1] 朱开永[1] 

机构地区：[1]中国矿业大学理学院,江苏徐州221008

出　　处：《中国矿业大学学报》2005年第3期405-408,共4页Journal of China University of Mining & Technology

摘　　要：从非线性数学期望的定义及其性质入手,通过与经典数学期望的比较,并利用经典的Lebesgue收敛定理和倒向随机微分方程解在L2意义下的连续性,提出并证明了被Eμ控制的非线性数学期望的Levi,Fatou及Lebesgue收敛定理,从而得到在适当条件下非线性数学期望在几乎处处意义下连续;同时指出这些结果对任意一个g-期望都成立.Levi, Fatou and Lebesgue convergent theorems on nonlinear mathematical expectation dominated by E~μ-expectation were put forward and proved based on the definition and properties of nonlinear mathematical expectation, the comparison with the classical mathematical expectation, the classical Lebesgue convergent theorem and the continuous property of the solution of a backward stochastic differential equation in L^2. Thus, the almost surely continuous property of nonlinear mathematical expectation under some proper conditions was obtained. At the same time, it was pointed out that these results are true for all g-expectations.

关 键 词：数学期望 非线性 Lebesgue收敛定理 微分方程解 G-期望 连续性 经典 倒向 

分 类 号：O211.67[理学—概率论与数理统计] O175.8[理学—数学]