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

Mohammud Foondun, Mathew Joseph, Shiu-Tang Li

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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.
Original languageEnglish
Pages (from-to)2855-2895
Number of pages41
JournalAnnals of Applied Probability
Volume28
Issue number5
Early online date28 Aug 2018
DOIs
Publication statusPublished - 31 Oct 2018

Keywords

  • stochastic PDEs
  • comparison theorems
  • colored noise

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