基于局部Lipschitz条件的非线性It随机微分方程的基本理论（英文）  

FUNDAMENTAL THEORY OF NONLINEAR ITO STOCHASTIC DIFFERENTIAL EQUATIONS UNDER THE LOCAL LIPSCHITZ CONDITION

作　　者：赵学艳[1] 邓飞其[1] 杨启贵[2] 

机构地区：[1]华南理工大学系统工程研究所,广州510640 [2]华南理工大学数学学院,广州510640

出　　处：《系统科学与数学》2016年第12期2164-2171,共8页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(61503142,61573156,61273126);中央高校基本科研业务费项目(x2zd-D2153620)资助课题

摘　　要：主要目的是在局部Lipschitz条件下建立非线性Ito随机微分方程的基本理论,包括解的存在性和非零性.过去文献中的局部Lipschitz条件被减弱为广义局部Lipschitz条件,其系数可以是局部、变系数、非线性的,在时间维上真正允许系数的时变性,在空间维上真正允许系数的非线性性.The main purpose of this paper is to establish the fundamental theory of nonlinear It6 stochastic differential equations under the Local Lipschitz condition, including the existence and non-zero property for the solutions. The local Lipschitz condition is weakened to the generalized local Lipschitz condition, which is local, variable and nonlinear, admits nearly arbitrary variability in the time and real non- linearity in the state.

关 键 词：Ito随机微分方程 局部LIPSCHITZ条件 存在性 非零性 

分 类 号：O211.63[理学—概率论与数理统计]