多维G-方程极值定理  

Extreme Value Theorem of Multidimensional G-Equation

作　　者：李洋 江继祥 张宇 许乾海 

机构地区：[1]上海理工大学理学院,上海

出　　处：《理论数学》2024年第5期140-144,共5页Pure Mathematics

摘　　要：本文基于G-期望空间理论,通过反证法,利用Hessian矩阵将G-方程的极值定理推广到多维空间和变系数的情况,得到了多维变系数G-方程极值在定义域边界取得的结论,在物理学、金融学以及计算数学领域有很高的实用性价值。This article is based on the theory of G-expected space and uses the method of proof to generalize the extreme value theorem of G-equations to multi-dimensional space and variable coefficient cases using Hessian matrix. The conclusion that the extreme values of multi-dimensional variable coefficient G-equations are obtained at the boundary of the domain is obtained, which has high practical value in the fields of physics, finance, and computational mathematics.

关 键 词：非线性期望 变系数G-方程 多维G-方程 HESSIAN矩阵 

分 类 号：G63[文化科学—教育学]