Wellposedness and numerical schemes for onedimensional McKeanVlasov equations and interacting particle systems with discontinuous drift
Abstract
In this paper, we first establish wellposedness results for onedimensional McKeanVlasov stochastic differential equations (SDEs) and related particle systems with a measuredependent 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 nonzero in a point of discontinuity of the drift, while we need to impose certain structural assumptions on the measuredependence of the drift. Second, we study EulerMaruyama type schemes for the particle system to approximate the solution of the onedimensional McKeanVlasov SDE. Here, we will prove strong convergence results in terms of the number of timesteps and number of particles. Due to the discontinuity of the drift, the convergence analysis is nonstandard and the usual strong convergence order $1/2$ known for the Lipschitz case cannot be recovered for all schemes.
 Publication:

arXiv eprints
 Pub Date:
 June 2020
 arXiv:
 arXiv:2006.14892
 Bibcode:
 2020arXiv200614892L
 Keywords:

 Mathematics  Probability;
 Mathematics  Numerical Analysis;
 65C20;
 65C30;
 65C35;
 60H30;
 60H35;
 60K40
 EPrint:
 33 pages, 4 figures