We extend Krylov's $L_p$-solvability theory to the Cauchy problem for systems of parabolic stochastic partial differential equations. Some additional integrability and regularity properties are also presented.

A class of linear degenerate second-order parabolic equations is considered in arbitrary domains. It is shown that these equations are solvable using special weighted Sobolev spaces in essentially the same way as the non-degenerate equations in $R^d$ are solved using…