Convergent Theorems for Nonlinear Mathematical Expectation
Zhu Kai-yong · Journal of China University of Mining and Technology · 2005
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.