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

da Costa, Conrado; Freitas Paulo da Costa, Bernardo; Valesin, Daniel

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Authors

Bernardo Freitas Paulo da Costa

Daniel Valesin



Abstract

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.

Citation

da Costa, C., Freitas Paulo da Costa, B., & Valesin, D. (2023). Reaction–Diffusion Models for a Class of Infinite-Dimensional Nonlinear Stochastic Differential Equations. Journal of Theoretical Probability, 36, 1059–1087. https://doi.org/10.1007/s10959-022-01187-9

Journal Article Type Article
Acceptance Date Jun 6, 2022
Online Publication Date Aug 8, 2022
Publication Date 2023-06
Deposit Date Sep 8, 2022
Publicly Available Date Mar 28, 2024
Journal Journal of Theoretical Probability
Print ISSN 0894-9840
Electronic ISSN 1572-9230
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 36
Pages 1059–1087
DOI https://doi.org/10.1007/s10959-022-01187-9
Public URL https://durham-repository.worktribe.com/output/1194863

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Publisher Licence URL
http://creativecommons.org/licenses/by/4.0/

Copyright 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 Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the 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 http://creativecommons.org/licenses/by/4.0/.




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