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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Mean field limits of spatially structured Hawkes p
rocesses - Eva LĂ¶cherbach (University of Paris 1 P
anthĂ©on-Sorbonne)
DTSTART;TZID=Europe/London:20220323T110000
DTEND;TZID=Europe/London:20220323T113000
UID:TALK171698AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/171698
DESCRIPTION:We consider spatially extended systems of interact
ing nonlinear Hawkesprocesses modeling e.g.large s
ystems of neurons placed in $\\R^d$ and study the
associated mean field limits. As the total number
of neurons tends to infinity\, we prove that the e
volution of a typical neuron\, attached to a given
spatial position\, can be described by a nonlinea
r limit differential equation driven by a Poisson
random measure which is of McKean-Vlasov type. The
limit process is described by a neural field equa
tion. As a consequence\, we provide a rigorous der
ivation of the neural field equation based on a th
orough mean field analysis. In a last part of the
talk we discuss the framework of diffusive scaling
s where the associated mean field limits are descr
ibed by conditional McKean-Vlasov type equations\,
related to the presence of common noise in the li
mit system. The talk is based on common work with
J. Chevallier\, A. Duarte\, X. Erny\, D. Loukianov
a and G. Ost. \;
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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