$W^{m,p}$-Solution ($p\geq2$) of Linear Degenerate Backward Stochastic   Partial Differential Equations in the Whole Space
  In this paper, we consider the backward Cauchy problem of linear degenerate stochastic partial differential equations. We obtain the existence and uniqueness results in Sobolev space $L^p(\Omega; C([0,T];W^{m,p}))$ with both $m\geq 1$ and $p\geq 2$ being arbitrary, without imposing the symmetry condition for the coefficient $\sigma$ of the gradient of the second unknown---which was introduced by Ma and Yong [Prob. Theor. Relat. Fields 113 (1999)] in the case of $p=2$. To illustrate the application, we give a maximum principle for optimal control of degenerate stochastic partial differential equations. 
Kai Du and Shanjian Tang and Qi Zhang
math.PR math.AP