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October 2018 An approximation result for a class of stochastic heat equations with colored noise
Mohammud Foondun, Mathew Joseph, Shiu-Tang Li
Ann. Appl. Probab. 28(5): 2855-2895 (October 2018). DOI: 10.1214/17-AAP1376

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 works of [Stoch. Stoch. Rep. 37 (1991) 225–245] and [Ann. Probab. 45 (2017) 377–403] among others. 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.

Citation

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Mohammud Foondun. Mathew Joseph. Shiu-Tang Li. "An approximation result for a class of stochastic heat equations with colored noise." Ann. Appl. Probab. 28 (5) 2855 - 2895, October 2018. https://doi.org/10.1214/17-AAP1376

Information

Received: 1 December 2016; Revised: 1 October 2017; Published: October 2018
First available in Project Euclid: 28 August 2018

zbMATH: 06974767
MathSciNet: MR3847975
Digital Object Identifier: 10.1214/17-AAP1376

Subjects:
Primary: 60H15
Secondary: 35K57

Rights: Copyright © 2018 Institute of Mathematical Statistics

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Vol.28 • No. 5 • October 2018
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