Reference request : existence and uniqueness of solution to a certain class of SPDE

Question

Is there any papers/reference for the existence and uniqueness of the following type of Stochastic Partial Differential Equations (perhaps a much larger class of SPDES containing the following) $$ dv(t,x)=\mu(x)\dfrac{\partial v}{\partial x}(t,x)dt+a\dfrac{\partial^2 v}{\partial x^2}(t,x)dt+b\dfrac{\partial v}{\partial x}dW_t. $$ Where $a$ and $b$ are constants and $\mu(x)$ is Lipschitz in $x$ or bounded by linear growth. The boundary condition is of the Dirichlet type and $W_t$ the usual Wiener process.

Answer 1

Section 3.7 of P.L. Chow's book on Stochastic Partial Differential Equations discusses this type of equations (only on a finite domain but I think that is what you want).