An approximation result for a class of stochastic heat equations with colored noise

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Foondun, Mohammud and Joseph, Mathew and Li, Shiu-Tang (2018) An approximation result for a class of stochastic heat equations with colored noise. Annals of Applied Probability, 28 (5). pp. 2855-2895. ISSN 1050-5164 (https://doi.org/10.1214/17-AAP1376)

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Abstract

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.

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