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2022 McKean-Vlasov equations with positive feedback through elastic stopping times
Ben Hambly, Julian Meier
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Electron. Commun. Probab. 27: 1-13 (2022). DOI: 10.1214/22-ECP482

Abstract

We prove existence and uniqueness of physical and minimal solutions to McKean-Vlasov equations with positive feedback through elastic stopping times. We do this by establishing a relationship between this problem and a problem with absorbing stopping times. We show convergence of a particle system to the McKean-Vlasov equation. Moreover, we establish convergence of the elastic McKean-Vlasov problem to the problem with absorbing stopping times and to a reflecting Brownian motion as the elastic parameter goes to infinity or zero respectively.

Funding Statement

This research has been supported by the EPSRC Centre for Doctoral Training in Mathematics of Random Systems: Analysis, Modelling and Simulation (EP/S023925/1).

Citation

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Ben Hambly. Julian Meier. "McKean-Vlasov equations with positive feedback through elastic stopping times." Electron. Commun. Probab. 27 1 - 13, 2022. https://doi.org/10.1214/22-ECP482

Information

Received: 21 March 2022; Accepted: 29 July 2022; Published: 2022
First available in Project Euclid: 29 August 2022

Digital Object Identifier: 10.1214/22-ECP482

Subjects:
Primary: 35K61 , 60H30 , 60K35

Keywords: contagion , McKean-Vlasov problem , Particle system , singular interactions

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