An approximation result for a class of stochastic heat equations with   colored noise
  We show that a large class of stochastic heat equations can be approximated by systems of interacting stochastic differential equations. As a consequence, we prove various comparison principles extending earlier results. Among other things, our results enable us to obtain sharp estimates on the moments of the solution. A main technical ingredient of our method is a local limit theorem which is of independent interest. 
Mohammud Foondun, Shiu-Tang Li and Mathew Joseph
math.PR