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SUMMARY:Mean field limits of spatially structured Hawkes processes - Eva L
 öcherbach (University of Paris 1 Panthéon-Sorbonne)
DTSTART:20220323T110000Z
DTEND:20220323T113000Z
UID:TALK171698@talks.cam.ac.uk
DESCRIPTION:We consider spatially extended systems of interacting nonlinea
 r Hawkesprocesses modeling e.g.large systems 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 evolution of a typical neuron\, att
 ached to a given spatial position\, can be described by a nonlinear limit 
 differential equation driven by a Poisson random measure which is of McKea
 n-Vlasov type. The limit process is described by a neural field equation. 
 As a consequence\, we provide a rigorous derivation of the neural field eq
 uation based on a thorough mean field analysis. In a last part of the talk
  we discuss the framework of diffusive scalings where the associated mean 
 field limits are described by conditional McKean-Vlasov type equations\, r
 elated to the presence of common noise in the limit system. The talk is ba
 sed on common work with J. Chevallier\, A. Duarte\, X. Erny\, D. Loukianov
 a and G. Ost.&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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