On existence and uniqueness of solutions to uncertain backward stochastic differential equations  

作　　者：FEI Wei-yin 

机构地区：[1]School of Mathematics and Physics,Anhui Polytechnic University

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2014年第1期53-66,共14页高校应用数学学报（英文版）（B辑）

基　　金：Supported by National Natural Science Foundation of China(71171003,71210107026);Anhui Natural Science Foundation(10040606003);Anhui Natural Science Foundation of Universities(KJ2012B019,KJ2013B023)

摘　　要：This paper is concerned with a class of uncertain backward stochastic differential equations （UBSDEs） driven by both an m-dimensional Brownian motion and a d-dimensional canonical process with uniform Lipschitzian coefficients. Such equations can be useful in mod- elling hybrid systems, where the phenomena are simultaneously subjected to two kinds of un- certainties： randomness and uncertainty. The solutions of UBSDEs are the uncertain stochastic processes. Thus, the existence and uniqueness of solutions to UBSDEs with Lipschitzian coeffi- cients are proved.This paper is concerned with a class of uncertain backward stochastic differential equations （UBSDEs） driven by both an m-dimensional Brownian motion and a d-dimensional canonical process with uniform Lipschitzian coefficients. Such equations can be useful in mod- elling hybrid systems, where the phenomena are simultaneously subjected to two kinds of un- certainties： randomness and uncertainty. The solutions of UBSDEs are the uncertain stochastic processes. Thus, the existence and uniqueness of solutions to UBSDEs with Lipschitzian coeffi- cients are proved.

关 键 词：Uncertain backward stochastic differential equations(UBSDEs) canonical process existence and uniqueness Lipschitzian condition martingale representation theorem 

分 类 号：O211.63[理学—概率论与数理统计] O211.6[理学—数学]