Notes on the Cauchy Problem for Backward Stochastic Partial Differential Equations

Kai Du; Qingxin Meng

paper

Notes on the Cauchy Problem for Backward Stochastic Partial Differential Equations

arXiv:0911.0077

Abstract

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 $H^{n}$ ( $= W_{2}^{n}$ ) under weaker assumptions than those used by X. Zhou [Journal of Functional Analysis 103, 275--293 (1992)]. As an application, a comparison theorem is obtained.

20 pages