  In this article, we construct weak solutions for a class of Stochastic PDEs
in the space of tempered distributions via Girsanov's theorem. It is to be
noted that our drift and diffusion coefficients $(L,A)$ of the considered
Stochastic PDE satisfy a Monotonicity type inequality, rather than Lipschitz
conditions. As such, we can not follow the usual infinite dimensional analysis
as described in \cite[sections 10.2 and 10.3]{MR3236753}. Instead, we exploit
related SDEs to obtain our desired result, and we point out an important
observation that the same Novikov condition is used in changing the Brownian
motion in both the SDEs and the Stochastic PDEs.
