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

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

[img]
Preview
Text (Foondun-etal-AAP-2018-An-approximation-result-for-a-class-of-stochastic-heat-equations)
Foondun_etal_AAP_2018_An_approximation_result_for_a_class_of_stochastic_heat_equations.pdf
Accepted Author Manuscript

Download (283kB)| Preview

    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.