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

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

doi:10.1007/s10959-022-01187-9

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

Conrado da Costa^*, Bernardo Freitas Paulo da Costa, Daniel Valesin

^*Corresponding author for this work

Probability and Statistics

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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.

Original language	English
Pages (from-to)	1059–1087
Number of pages	29
Journal	Journal of theoretical probability
Volume	36
Early online date	8-Aug-2022
DOIs	https://doi.org/10.1007/s10959-022-01187-9
Publication status	Published - Jun-2023

Keywords

Martingale problems
Reaction–diffusion models
Scaling limits of particle systems
Thermodynamic limit

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Reaction–Diffusion Models for a Class of Infinite-Dimensional Nonlinear Stochastic Differential EquationsFinal publisher's version, 469 KBLicence: CC BY

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title = "Reaction–Diffusion Models for a Class of Infinite-Dimensional Nonlinear Stochastic Differential Equations",

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 = "Martingale problems, Reaction–diffusion models, Scaling limits of particle systems, Thermodynamic limit",

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AU - da Costa, Conrado

AU - Freitas Paulo da Costa, Bernardo

AU - Valesin, Daniel

PY - 2023/6

Y1 - 2023/6

N2 - 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.

AB - 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.

KW - Martingale problems

KW - Reaction–diffusion models

KW - Scaling limits of particle systems

KW - Thermodynamic limit

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EP - 1087

JO - Journal of theoretical probability

JF - Journal of theoretical probability

ER -

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

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Keywords

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