In this paper, we first establish well-posedness results of McKean-Vlasov stochastic differential equations (SDEs) and related particle systems with a  drift coefficient that is discontinuous in the spatial component . The analysis is restricted to the one-dimensional case, and we only require a fairly mild condition on the diffusion coefficient, namely to be non-zero in a point of discontinuity  , while we need to impose certain structural assumptions on the measure-dependence of the drift. Second, we study fully implementable Euler-Maruyama-type schemes for the particle system to approximate the solution of the  McKean-Vlasov SDEs . Here, we will prove strong convergence results in terms of  number of time-steps and number of particles. Due to the discontinuity of the drift, the convergence analysis is non-standard and the usual 1/2 strong convergence order  known for the Lipschitz case cannot be recovered for all presented schemes.
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 structural assumptions on the measure-dependence of the drift. Second, we study fully implementable Euler-Maruyama type schemes for the particle system to approximate the solution of the one-dimensional McKean-Vlasov SDE . Here, we will prove strong convergence results in terms of the number of time-steps and number of particles. Due to the discontinuity of the drift, the convergence analysis is non-standard and the usual strong convergence order 1/2 known for the Lipschitz case cannot be recovered for all schemes.
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presented