Notes on the Cauchy Problem for Backward Stochastic Partial Differential Equations

Details Notes on the Cauchy Problem for Backward Stochastic Partial Differential Equations Notes on the Cauchy Problem for Backward Stochastic Partial Differential Equations

2009-11-02

arxiv.org/abs/0911.0077v3

Mathematics

Probability

20 pages

Scientific paper

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 $H^n$ ($=W^n_2$) 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.

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