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

Fabian A. Harang, Avi Mayorcas

Research output: Contribution to journalArticlepeer-review

2 Citations (SciVal)

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.

Original languageEnglish
Pages (from-to)499-540
Number of pages42
JournalStochastic Processes and their Applications
Volume159
Early online date16 Feb 2023
DOIs
Publication statusPublished - 1 May 2023

Bibliographical note

Funding Information:
We are grateful to the anonymous referees for their helpful comments which have greatly improved the manuscript. FH gratefully acknowledges financial support from the STORM project 274410 , funded by the Research Council of Norway . AM was supported by the EPSRC, UK Centre For Doctoral Training in Partial Differential Equations: Analysis and Applications [grant number EP/L015811/1 ].

Publisher Copyright:
© 2023

Funding

We are grateful to the anonymous referees for their helpful comments which have greatly improved the manuscript. FH gratefully acknowledges financial support from the STORM project 274410 , funded by the Research Council of Norway . AM was supported by the EPSRC, UK Centre For Doctoral Training in Partial Differential Equations: Analysis and Applications [grant number EP/L015811/1 ].

Keywords

  • Averaged fields
  • Interacting particle systems
  • Propagation of chaos
  • Regularisation by noise

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Applied Mathematics

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