Homogenization of a stochastic viscous transport equation

In the present paper we prove an homogenisation result for a locally perturbed transport stochastic equation. The model is similar to the stochastic Burgers' equation and it is inspired by the LWR model. Therefore, the interest in studying this equation comes from it's application for traffic flow modelling. In the first part of paper we study the inhomogeneous equation. More precisely we give an existence and uniqueness result for the solution. The technical difficulties of this part come from the presence of the function \begin{document}$ \varphi $\end{document} under assumptions coherent for the model, which is giving the inhomogeneity with respect to the space variable, not present in the classical results. The second part of the paper is the homogenisation result in space.