Reaction-diffusion models for a class of infinite-dimensional non-linear stochastic differential equations

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

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arXiv · 2004.12975

Reaction-diffusion models for a class of infinite-dimensional non-linear stochastic differential equations

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

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Abstract

We establish the existence of solutions to a class of non-linear stochastic differential equation 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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Conrado da Costa, Bernardo Freitas Paulo da Costa, Daniel Valesin. 2020-04-27. Reaction-diffusion models for a class of infinite-dimensional non-linear stochastic differential equations. https://arxiv.org/abs/2004.12975

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