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

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 s...

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Bibliographic Details
Published in:	Journal of theoretical probability Vol. 36; no. 2; pp. 1059 - 1087
Main Authors:	da Costa, Conrado, Freitas Paulo da Costa, Bernardo, Valesin, Daniel
Format:	Journal Article
Language:	English
Published:	New York Springer US 01-06-2023 Springer Nature B.V
Subjects:	Differential equations Martingales Mathematics Mathematics and Statistics Probability Theory and Stochastic Processes Statistics Martingale problems 60H10 Reaction–diffusion models Scaling limits of particle systems Thermodynamic limit 82B20 60J25 60K35
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Summary:	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.
ISSN:	0894-9840 1572-9230
DOI:	10.1007/s10959-022-01187-9