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 language | English |
|---|---|
| Pages (from-to) | 499-540 |
| Number of pages | 42 |
| Journal | Stochastic Processes and their Applications |
| Volume | 159 |
| Early online date | 16 Feb 2023 |
| DOIs | |
| Publication status | Published - 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