common noise 1integrate-and-fire neurons 1mckean-vaserov 1mean-field limit 1refractory period 1stochastic fokker-planck equation 1
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math.PR2026
Probabilistic estimates for a system of noisy integrate-and-fire neurons
Ben Hambly, Aldaïr Petronilia, Christoph Reisinger +1
In this note, we establish various probabilistic estimates for an interacting particle system that describes the evolution of the membrane potentials in a network of excitatory int…
math.PR2025
Contagious McKean--Vlasov problems with common noise: from smooth to singular feedback through hitting times
Ben Hambly, Aldaïr Petronilia, Christoph Reisinger +2
We consider a family of McKean--Vlasov equations arising as the large particle limit of a system of interacting particles on the positive half-line with common noise and feedback.…