倒向随机Volterra积分方程适应解的表示

Representation of adapted solutions to backward stochastic Volterra integral equations

倒向随机Volterra积分方程可以看作(确定性)Volterra积分方程和倒向随机微分方程的推广,在随机最优控制理论和数学金融学中有诸多应用.本文利用正倒向随机微分方程适应解表示的思想,得到所研究的一类倒向随机Volterra积分方程适应解的表示.这样的结果对研究适应解的正则性以及数值计算有重要的意义.

In this paper,we establish a representation for the backward components of the adapted solution of a backward stochastic Volterra integral equation,in terms of the solutions to a partial differential equation and a forward stochastic differential equation.