A revisit to W2n-theory of super-parabolic backward stochastic partial differential equations in RdRd

Backward stochastic partial differential equations of parabolic type with variable coefficients are considered in the whole Euclidean space. Improved existence and uniqueness results are given in the Sobolev space HnHn (=W2n) under weaker assumptions than those used by X. Zhou [X. Zhou, A duality analysis on stochastic partial differential equations, J. Funct. Anal. 103 (1992) 275–293]. As an application, a comparison theorem is obtained.