McKean-Vlasov Equations with Positive Feedback through Elastic Stopping Times
Probability
2022-03-22 v1
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.
Keywords
Cite
@article{arxiv.2203.10787,
title = {McKean-Vlasov Equations with Positive Feedback through Elastic Stopping Times},
author = {Ben Hambly and Julian Meier},
journal= {arXiv preprint arXiv:2203.10787},
year = {2022}
}
Comments
13 pages