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

2020/04/27 by da Costa, Conrado, da Costa, Bernardo Freitas Paulo, Valesin, Daniel
#60H10 #60J25 (Primary) #60K35 #82B20 (Secondary) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2004.12975

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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