WHITE-NOISE DRIVEN PARABOLIC SPDES WITH MEASURABLE DRIFT

We prove existence and uniqueness of the solution of a white noise dri ven parabolic SPDE, in case the drift is measurable and satisfies a '' one sided linear growth condition,'' and the diffusion coefficient is nondegenerate, has a locally Lipschitz derivative, and satisfies a lin ear growth condition. The proof combines arguments similar to those of Gyongy and Pardoux together with an estimate of the density of the so lution of the equation without drift, which is obtained with the help of the Malliavin calculus. (C) 1994 Academic Press, Inc.