Show simple item record

dc.contributor.authorHaji-Ali, Abdul-Lateef
dc.contributor.authorHoel, Håkon
dc.contributor.authorTempone, Raul
dc.date.accessioned2021-01-06T09:04:45Z
dc.date.available2021-01-06T09:04:45Z
dc.date.issued2021-01-04
dc.identifier.urihttp://hdl.handle.net/10754/666829
dc.description.abstractBy 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.publisherarXiv
dc.relation.urlhttps://arxiv.org/pdf/2101.00886
dc.rightsArchived with thanks to arXiv
dc.titleA simple approach to proving the existence, uniqueness, and strong and weak convergence rates for a broad class of McKean--Vlasov equations
dc.typePreprint
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentComputer, Electrical and Mathematical Science and Engineering (CEMSE) Division
dc.contributor.departmentStochastic Numerics Research Group
dc.eprint.versionPre-print
dc.contributor.institutionHeriot-Watt University, Edinburgh, UK.
dc.contributor.institutionRWTH Aachen University, Germany.
dc.identifier.arxivid2101.00886
kaust.personTempone, Raul
refterms.dateFOA2021-01-06T09:19:47Z


Files in this item

Thumbnail
Name:
Preprintfile1.pdf
Size:
403.7Kb
Format:
PDF
Description:
Pre-print

This item appears in the following Collection(s)

Show simple item record