随机单调条件下一般化倒向随机微分方程的适应解  

Adapted Solutions of Generalized BSDE with Stochastic Monotone Coefficients

作　　者：谢臻赟[1] 夏宁茂[1] 

机构地区：[1]华东理工大学数学系,上海200237

出　　处：《应用数学学报》2009年第3期555-569,共15页Acta Mathematicae Applicatae Sinica

摘　　要：本文讨论了如下一般化倒向随机微分方程适应解的存在唯一性问题,■其中W_s为d-维标准Wiener过程,A_s为一维零初值的F_s-循序可测增过程.我们通过构造函数逼近序列的方法证明了,在系数函数f和g关于Y满足随机单调,f关于Z满足随机Lipschitz条件下,方程存在唯一适应解.In this paper, we study the solution of a Generalized Backward Stochastic Differential Equation：Yt=ζ＋∫t^Tf（s,Ys,Zs）ds-∫t^Tg（s,Ys）dAs-∫t^TZsdWs,0≤t≤Twhere Ws is a d-dimensional standard Wiener process, As is a one-dimensional increasing .Fs-progressively measurable process satisfying A0 = 0. By using a series of approximate equations, we prove the existence and uniqueness of the adapted solutions when the coefficients f and 9 satisfy a stochastic monotonic condition in Y, and f satisfies a stochastic Lipschitz condition in Z.

关 键 词：一般化倒向随机微分方程 随机单调 存在唯一性 

分 类 号：O211.63[理学—概率论与数理统计]