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- W2598312936 abstract "We consider spatially extended systems of interacting nonlinear Hawkes processes modeling 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, attached to a given spatial position, can be described by a nonlinear limit differential equation driven by a Poisson random measure. The limit process is described by a neural field equation. As a consequence, we provide a rigorous derivation of the neural field equation based on a thorough mean field analysis." @default.
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- W2598312936 date "2019-01-01" @default.
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- W2598312936 title "Mean field limits for nonlinear spatially extended Hawkes processes with exponential memory kernels" @default.
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- W2598312936 doi "https://doi.org/10.1016/j.spa.2018.02.007" @default.
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