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We extend a model of positive feedback and contagion in large mean-field systems, by introducing a common source of noise driven by Brownian motion.
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Response of integrate-and-fire neurons to noisy inputs filtered by synapses with arbitrary time scales: firing rate and correlations
R. Moreno-Bote and N. Parga · 2010
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Analysis of non-linear noisy integrate & fire neuron models: blow-up and steady states
M.J. Cáceres, J.A. Carrillo and B. Perthame · 2011
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Classical solutions for a nonlinear Fokker–Planck equation arising in computational neuroscience
J.A. Carrillo, M.D.M. González, M.P. Gualdani and M.E. Schonbek · 2013
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Qualitative properties of solutions for the noisy integrate and fire model in computational neuroscience
J.A. Carrillo, B. Perthame, D. Salort and D. Smets · 2015
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Global solvability of a networked integrate-and-fire model of McKean–Vlasov type, Annals of Applied Probability
F. Delarue, J. Inglis, S. Rubenthaler and E. Tanré · 2015
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Particle systems with singular mean-field self-excitation. Application to neuronal networks, Stochastic Processes and their Applications 125(6): 2451–2492, 2015
F. Delarue, J. Inglis, S. Rubenthaler and E. Tanré · 2015
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Probabilistic Theory of Mean Field Games with Applications II. Mean Field Games with Common Noise and Master Equations
R. Carmona and F. Delarue · 2018
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Ubiquity of collective irregular dynamics in balanced networks of spiking neurons Chaos: An Interdisciplinary Journal of Nonlinear Science , 28(8), 2018
E. Ullner, A. Politi and A. Torcini · 2018
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F. Delarue, S. Nadtochyi, and M. Shkolnikov · 2019
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A McKean–Vlasov equation with positive feedback and blow-ups
B. Hambly, S. Ledger and A. Søjmark · 2019
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An SPDE model for systemic risk with endogenous contagion. Finance and Stochastics 23(3): 535–594, 2019
B. Hambly and A. Søjmark · 2019
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Uniqueness of contagious McKean–Vlasov systems in the weak feedback regime
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