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

Conrado Costa (), Bernardo Freitas Paulo da Costa and Daniel Valesin
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Conrado Costa: Mathematical Sciences & Computer Science Building
Bernardo Freitas Paulo da Costa: Universidade Federal do Rio de Janeiro, Centro de Tecnologia Bloco C - Av. Athos da Silveira Ramos
Daniel Valesin: University of Groningen

Journal of Theoretical Probability, 2023, vol. 36, issue 2, 1059-1087

Abstract: 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.

Keywords: Reaction–diffusion models; Scaling limits of particle systems; Martingale problems; Thermodynamic limit; 60J25; 60H10; 60K35; 82B20 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10959-022-01187-9

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