A simple approach to proving the existence, uniqueness, and strong and weak convergence rates for a broad class of McKean--Vlasov equations
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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