  In this article, using DiPerna-Lions theory \cite{Di-Li}, we investigate
linear second order stochastic partial differential equations with unbounded
and degenerate non-smooth coefficients, and obtain several conditions for
existence and uniqueness. Moreover, we also prove the $L^1$-integrability and a
general maximal principle for generalized solutions of SPDEs. As applications,
we study nonlinear filtering problem and also obtain the existence and
uniqueness of generalized solutions for a degenerate nonlinear SPDE.
