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

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  • Harang, Fabian A.
  • Mayorcas, Avi

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.

Suggested Citation

  • Harang, Fabian A. & Mayorcas, Avi, 2023. "Pathwise regularisation of singular interacting particle systems and their mean field limits," Stochastic Processes and their Applications, Elsevier, vol. 159(C), pages 499-540.
    • Handle: RePEc:eee:spapps:v:159:y:2023:i:c:p:499-540
    DOI: 10.1016/j.spa.2023.02.005
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    References listed on IDEAS

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    1. Coghi, Michele & Nilssen, Torstein, 2021. "Rough nonlocal diffusions," Stochastic Processes and their Applications, Elsevier, vol. 141(C), pages 1-56.
    2. Catellier, R. & Gubinelli, M., 2016. "Averaging along irregular curves and regularisation of ODEs," Stochastic Processes and their Applications, Elsevier, vol. 126(8), pages 2323-2366.
    3. Flandoli, F. & Gubinelli, M. & Priola, E., 2011. "Full well-posedness of point vortex dynamics corresponding to stochastic 2D Euler equations," Stochastic Processes and their Applications, Elsevier, vol. 121(7), pages 1445-1463, July.
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