非利普希茨条件下连续局部鞅驱动的集值随机微分方程  

Stochastic Set Differential Equations Driven by Local Martingales under the Non-Lipschitzian Condition

作　　者：费为银[1] 梁勇[1] 

机构地区：[1]安徽工程大学数理学院,芜湖241000

出　　处：《数学学报（中文版）》2013年第4期561-574,共14页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(71171003);安徽省自然科学基金(090416225);安徽省高校自然科学基金重点资助项目(KJ2010A037)

摘　　要：研究了非利普希茨条件下连续局郎鞅驱动的集值随机微分方程.这样的方程在一类随机现象的结果是多值的随机系统建模中是有用的.进而在非利普希茨条件下,集值随机微分方程解的存在唯一性得以证明.还探讨了集值随机微分方程解的稳定性.In this paper, a class of stochastic set differential equations （SSDEs） driven by a continuous local martingale under the non-Lipschitzian condition is studied. Such equations can be useful in modelling of stochastic systems, where the phenomena are subjected to a random outcome being multivalued. The solutions of SSDEs are the set- valued stochastic processes. Thus, the existence and uniqueness of solutions to SSDEs under the non-Lipschitzian condition is first proven. Then the stability of solutions to SSDEs is investigated.

关 键 词：集值随机微分方程 伊藤随机积分 局部鞅 非利普希茨条件 BIHARI不等式 

分 类 号：O211.63[理学—概率论与数理统计]