Necessary and sufficient condition for the comparison theorem of multidimensional anticipated backward stochastic differential equations  

作　　者：XU XiaoMing 

机构地区：[1]School of Mathematical Sciences, Nanjing Normal University, Nanjing 210046, China

出　　处：《Science China Mathematics》2011年第2期301-310,共10页中国科学：数学（英文版）

摘　　要：Anticipated backward stochastic differential equations, studied the first time in 2007, are equations of the following type:{-dY t = f(t1, Y t1 , Z t1 , Y t+δ(t) , Z t+ζ(t) )dt Z t dB t1 , t ∈ [0, T ], Y t = ξ t1 , t ∈ [T, T + K], Z t = η t1 , t ∈ [T, T + K].In this paper, we give a necessary and sufficient condition under which the comparison theorem holds for multidimensional anticipated backward stochastic differential equations with generators independent of the anticipated term of Z.Anticipated backward stochastic differential equations, studied the first time in 2007, are equations of the following type：{-dY t = f（t1, Y t1 , Z t1 , Y t＋δ（t） , Z t＋ζ（t） ）dt Z t dB t1 , t ∈ [0, T ], Y t = ξ t1 , t ∈ [T, T ＋ K], Z t = η t1 , t ∈ [T, T ＋ K].In this paper, we give a necessary and sufficient condition under which the comparison theorem holds for multidimensional anticipated backward stochastic differential equations with generators independent of the anticipated term of Z.

关 键 词：comparison theorem multidimensional anticipated backward stochastic differential equation necessary and sufficient condition 

分 类 号：O211.63[理学—概率论与数理统计] O211.61[理学—数学]