具有Osgood型生成元的多维倒向重随机微分方程  

Multidimensional backward doubly stochastic differential equations with generators of Osgood type

作　　者：王先飞[1] 江龙[1] 马娇娇[1] 

机构地区：[1]中国矿业大学理学院,江苏徐州221116

出　　处：《山东大学学报（理学版）》2015年第8期24-33,共10页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11371362)

摘　　要：研究了一类多维倒向重随机微分方程,其生成元f关于y满足Osgood条件,且生成元g关于y满足一类新的非Lipschitz条件。建立了该类方程的一个解的存在唯一性定理和一个稳定性定理,并给出了该类方程在一维情形下解的比较定理。A class of multidimensional backward doubly stochastic differential equations whose generator f satisfies the Osgood condition in y and generator g satisfies non-Lipschitz condition in y was studied. An existence and uniqueness theorem and a stability theorem of solutions for this kind of equations were established, and a comparison theorem for solution of the class of one-dimensional situation was proposed.

关 键 词：倒向重随机微分方程 Osgood条件 存在唯一性定理 稳定性定理 比较定理 

分 类 号：O211[理学—概率论与数理统计]