Backward Doubly Stochastic Differential Equations with Jumps and Stochastic Partial Differential-Integral Equations  

作　　者：Qingfeng ZHU Yufeng SHI 

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

出　　处：《Chinese Annals of Mathematics,Series B》2012年第1期127-142,共16页数学年刊（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China (Nos. 10771122,11071145);the Shandong Provincial Natural Science Foundation of China (No. Y2006A08);the Foundation for Innovative Research Groups of National Natural Science Foundation of China (No. 10921101);the National Basic Research Program of China (the 973 Program) (No. 2007CB814900);the Independent Innovation Foundation of Shandong University (No. 2010JQ010)

摘　　要：Backward doubly stochastic differential equations driven by Brownian motions and Poisson process （BDSDEP） with non-Lipschitz coefficients on random time interval are studied. The probabilistic interpretation for the solutions to a class of quasilinear stochastic partial differential-integral equations （SPDIEs） is treated with BDSDEP. Under non-Lipschitz conditions, the existence and uniqueness results for measurable solutions to BDSDEP are established via the smoothing technique. Then, the continuous depen- dence for solutions to BDSDEP is derived. Finally, the probabilistic interpretation for the solutions to a class of quasilinear SPDIEs is given.

关 键 词：Backward doubly stochastic differential equations Stochastic partialdifferential-integral equations Random measure Poisson process 

分 类 号：O211.63[理学—概率论与数理统计] O175.5[理学—数学]