New particle representations for ergodic McKean-Vlasov SDEs

Houssam Alrachid (1) , Mireille Bossy (2) , Cristiano Ricci (3) , Lukasz Szpruch (4)

1 IDP - Institut Denis Poisson
2 TOSCA - TO Simulate and CAlibrate stochastic models
3 UniFI - Università degli Studi di Firenze = University of Florence = Université de Florence
4 School of Mathematics - University of Edinburgh

The aim of this paper is to introduce several new particle representations for \textit{ergodic} McKean-Vlasov SDEs. We construct new algorithms by leveraging recent progress in weak convergence analysis of interacting particle system. We present detailed analysis of errors and associated costs of various estimators, highlighting key differences between long-time simulations of linear (classical SDEs) versus non-linear (Mckean-Vlasov SDEs) process.

Domaines: Analyse numérique [math.NA]

Houssam Alrachid, Mireille Bossy, Cristiano Ricci, Lukasz Szpruch. New particle representations for ergodic McKean-Vlasov SDEs. ESAIM: Proceedings and Surveys, 2019, CEMRACS 2017 - Numerical methods for stochastic models: control, uncertainty quantification, mean-field, 65, pp.68-83. ⟨10.1051/proc/201965068⟩. ⟨hal-02059785⟩