Pathwise regularisation of singular interacting particle systems and their mean field limits

Fabian A. Harang and Avi Mayorcas

Stochastic Processes and their Applications, 2023, vol. 159, issue C, 499-540

Abstract: We investigate the regularising effect of certain perturbations by noise in singular interacting particle systems under the mean field scaling. In particular, we show that the addition of a suitably irregular path can regularise these dynamics and we recover the McKean–Vlasov limit under very broad assumptions on the interaction kernel; only requiring it to be controlled in a possibly distributional Besov space. In the particle system we include two sources of randomness, a common noise path Z which regularises the dynamics and a family of idiosyncratic noises, which we only assume to converge in mean field scaling to a representative noise in the McKean–Vlasov equation.

Keywords: Regularisation by noise; Interacting particle systems; Propagation of chaos; Averaged fields (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:159:y:2023:i:c:p:499-540

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DOI: 10.1016/j.spa.2023.02.005

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