dc.contributor.author Haji-Ali, Abdul-Lateef dc.contributor.author Hoel, Håkon dc.contributor.author Tempone, Raul dc.date.accessioned 2021-01-06T09:04:45Z dc.date.available 2021-01-06T09:04:45Z dc.date.issued 2021-01-04 dc.identifier.uri http://hdl.handle.net/10754/666829 dc.description.abstract By employing a system of interacting stochastic particles as an approximation of the McKean--Vlasov equation and utilizing classical stochastic analysis tools, namely It\^o's formula and Kolmogorov--Chentsov continuity theorem, we prove the existence and uniqueness of strong solutions for a broad class of McKean--Vlasov equations. Considering an increasing number of particles in the approximating stochastic particle system, we also prove the $L^p$ strong convergence rate and derive the weak convergence rates using the Kolmogorov backward equation and variations of the stochastic particle system. Our convergence rates were verified by numerical experiments which also indicate that the assumptions made here and in the literature can be relaxed. dc.publisher arXiv dc.relation.url https://arxiv.org/pdf/2101.00886 dc.rights Archived with thanks to arXiv dc.title A simple approach to proving the existence, uniqueness, and strong and weak convergence rates for a broad class of McKean--Vlasov equations dc.type Preprint dc.contributor.department Applied Mathematics and Computational Science Program dc.contributor.department Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division dc.contributor.department Stochastic Numerics Research Group dc.eprint.version Pre-print dc.contributor.institution Heriot-Watt University, Edinburgh, UK. dc.contributor.institution RWTH Aachen University, Germany. dc.identifier.arxivid 2101.00886 kaust.person Tempone, Raul refterms.dateFOA 2021-01-06T09:19:47Z
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