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.
- stochastic PDEs
- comparison theorems
- colored noise
Foondun, M., Joseph, M., & Li, S-T. (2018). An approximation result for a class of stochastic heat equations with colored noise. Annals of Applied Probability, 28(5), 2855-2895. https://doi.org/10.1214/17-AAP1376