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Reaction–Diffusion Models for a Class of Infinite-Dimensional Nonlinear Stochastic Differential Equations

da Costa, Conrado and Freitas Paulo da Costa, Bernardo and Valesin, Daniel (2022) 'Reaction–Diffusion Models for a Class of Infinite-Dimensional Nonlinear Stochastic Differential Equations.', Journal of theoretical probability. .


We establish the existence of solutions to a class of nonlinear stochastic differential equations of reaction–diffusion type in an infinite-dimensional space, with diffusion corresponding to a given transition kernel. The solution obtained is the scaling limit of a sequence of interacting particle systems and satisfies the martingale problem corresponding to the target differential equation.

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Publisher statement:Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit
Date accepted:06 June 2022
Date deposited:08 September 2022
Date of first online publication:08 August 2022
Date first made open access:08 September 2022

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