The Annals of Applied Probability

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

Mohammud Foondun, Mathew Joseph, and 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 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.

Article information

Source
Ann. Appl. Probab., Volume 28, Number 5 (2018), 2855-2895.

Dates
Received: December 2016
Revised: October 2017
First available in Project Euclid: 28 August 2018

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1535443236

Digital Object Identifier
doi:10.1214/17-AAP1376

Mathematical Reviews number (MathSciNet)
MR3847975

Zentralblatt MATH identifier
06974767

Subjects
Primary: 60H15: Stochastic partial differential equations [See also 35R60]
Secondary: 35K57: Reaction-diffusion equations

Keywords
Stochastic PDEs comparison theorems colored noise

Citation

Foondun, Mohammud; Joseph, Mathew; Li, Shiu-Tang. An approximation result for a class of stochastic heat equations with colored noise. Ann. Appl. Probab. 28 (2018), no. 5, 2855--2895. doi:10.1214/17-AAP1376. https://projecteuclid.org/euclid.aoap/1535443236


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