Forward-backward doubly stochastic differential equations and related stochastic partial differential equations  

作　　者：ZHU QingFeng SHI YuFeng 

机构地区：[1]School of Mathematic and Quantitative Economics, Shandong University of Finance and Economics, Jinan 250014, China [2]School of Mathematics, Shandong University, Jinan 250100, China

出　　处：《Science China Mathematics》2012年第12期2517-2534,共18页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant Nos. 10771122, 11071145, 10921101 and 11231005);Natural Science Foundation of Shandong Province of China(Grant No. Y2006A08);National Basic Research Program of China (973 Program) (Grant No. 2007CB814900);Independent Innovation Foundation of Shandong University (Grant No. 2010JQ010)

摘　　要：The notion of bridge is introduced for systems of coupled forward-backward doubly stochastic differential equations （FBDSDEs）. It is proved that if two FBDSDEs are linked by a bridge, then they have the same unique solvability. Consequently, by constructing appropriate bridges, we obtain several classes of uniquely solvable FBDSDEs. Finally, the probabilistie interpretation for the solutions to a class of quasilinear stochastic partial differential equations （SPDEs） combined with algebra equations is given. One distinctive character of this result is that the forward component of the FBDSDEs is coupled with the backvzard variable.The notion of bridge is introduced for systems of coupled forward-backward doubly stochastic differential equations (FBDSDEs). It is proved that if two FBDSDEs are linked by a bridge, then they have the same unique solvability. Consequently, by constructing appropriate bridges, we obtain several classes of uniquely solvable FBDSDEs. Finally, the probabilistic interpretation for the solutions to a class of quasilinear stochastic partial differential equations (SPDEs) combined with algebra equations is given. One distinctive character of this result is that the forward component of the FBDSDEs is coupled with the backward variable.

关 键 词：forward-backward doubly stochastic differential equations BRIDGE measurable solution stochasticpartial differential equations 

分 类 号：O211.63[理学—概率论与数理统计] O175.25[理学—数学]