MULTI-DIMENSIONAL REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS AND THE COMPARISON THEOREM  

作　　者：吴臻 消华 

机构地区：[1]School of Mathematics,Shandong University [2]School of Mathematics and Statistics,Shandong University at Weihai

出　　处：《Acta Mathematica Scientia》2010年第5期1819-1836,共18页数学物理学报（B辑英文版）

基　　金：the National Natural Science Foundation(10371067);the National Basic Research Program of China(973 Program,2007CB814904);the Natural Science Foundation of Shandong Province(Z2006A01);the Doctoral Fund of Education Ministry of China,and Youth Growth Foundation of Shandong University at Weihai, P.R.China. Xiao acknowledges the Natural Science Foundation of Shandong Province (ZR2009AQ017);Independent Innovation Foundation of Shandong University,IIFSDU

摘　　要：In this article, we study the multi-dimensional reflected backward stochastic differential equations. The existence and uniqueness result of the solution for this kind of equation is proved by the fixed point argument where every element of the solution is forced to stay above the given stochastic process, i.e., multi-dimensional obstacle, respectively. We also give a kind of multi-dimensional comparison theorem for the reflected BSDE and then use it as the tool to prove an existence result for the multi-dimensional reflected BSDE where the coefficient is continuous and has linear growth.In this article, we study the multi-dimensional reflected backward stochastic differential equations. The existence and uniqueness result of the solution for this kind of equation is proved by the fixed point argument where every element of the solution is forced to stay above the given stochastic process, i.e., multi-dimensional obstacle, respectively. We also give a kind of multi-dimensional comparison theorem for the reflected BSDE and then use it as the tool to prove an existence result for the multi-dimensional reflected BSDE where the coefficient is continuous and has linear growth.

关 键 词：backward stochastic differential equations comparison theorem local time 

分 类 号：O211.63[理学—概率论与数理统计] O435.1[理学—数学]