We discuss the 2009 work of Chabanol and Duchon, who considered Burgers equation $u_t + uu_x = f$ where the forcing $f(x,t)$ is Brownian in space and white noise in time, and defined a statistical notion of solution for this problem. We will see that if $u(x,0)$ is a L\'{e}vy process of finite variance without positive jumps that this property is preserved at later time and derive a PDE for the...