Pathwise regularisation of singular interacting particle systems and their mean field limits. (English) Zbl 1509.60173
Summary: 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.
MSC:
| 60K35 | Interacting random processes; statistical mechanics type models; percolation theory |
| 35Q79 | PDEs in connection with classical thermodynamics and heat transfer |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 60H50 | Regularization by noise |
Keywords:
regularisation by noise; interacting particle systems; propagation of chaos; averaged fieldsReferences:
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