带跳的分数倒向重随机微分方程及相应的随机积分偏微分方程

本文首次把Poisson随机测度引入分数倒向重随机微分方程,基于可料的Girsanov变换证明由Brown运动、Poisson随机测度和Hurst参数在(1/2,1)范围内的分数Brown运动共同驱动的半线性倒向重随机微分方程解的存在唯一性.在此基础上,本文定义一类半线性随机积分偏微分方程的随机黏性解,并证明该黏性解由带跳分数倒向重随机微分方程的解唯一地给出,对经典的黏性解理论作出有益的补充.

Fractional backward doubly stochastic differential equations with jumps and the related SIPDEs

We study semilinear backward doubly stochastic differential equations driven by a Brownian motion, a Poisson random measure and a fractional Brownian motion with Hurst parameter in （1/2, 1）. We obtain the existence and uniqueness of the solutions. We also prove that the solution of semilinear fractional backward doubly stochastic differential equation with jumps defines the unique stochastic viscosity solution of a semilinear stochastic integral-partial differential equation driven by a fractional Brownian motion.