Backward Stochastic Partial Differential Equations in Hölder Spaces

Wenning Wei (Fudan University)
Thursday, December 3, 2015 - 5:15pm
HU Berlin, Rudower Chaussee 25, Room 1.115

My talk is concerned with solution in Hölder spaces for linear and semi-linear backward stochastic partial differential equations (BSPDEs) of super-parabolic type. The pair of unknown functional variables are viewed as deterministic time-space functionals, but take values in Banach spaces of random (vector) variables or processes. We define suitable functional Hölder spaces for them and give some inequalities among these Hölder norms. The existence, uniqueness as well as the regularity of solutions are proved for BSPDEs, which contain new assertions even on deterministic PDEs.