Well-posedness and numerical schemes for one-dimensional McKean–Vlasov equations and interacting particle systems with discontinuous drift

@article{Leobacher2022WellposednessAN,
  title={Well-posedness and numerical schemes for one-dimensional McKean–Vlasov equations and interacting particle systems with discontinuous drift},
  author={Gunther Leobacher and Christoph Reisinger and Wolfgang Stockinger},
  journal={BIT Numerical Mathematics},
  year={2022},
  volume={62},
  pages={1505 - 1549}
}
In this paper, we first establish well-posedness results for one-dimensional McKean–Vlasov stochastic differential equations (SDEs) and related particle systems with a measure-dependent drift coefficient that is discontinuous in the spatial component, and a diffusion coefficient which is a Lipschitz function of the state only. We only require a fairly mild condition on the diffusion coefficient, namely to be non-zero in a point of discontinuity of the drift, while we need to impose certain… 

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