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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}
}

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13 pages