33 citations · 88 across the 14 of their papers we have counts for
8 papers · 1 filter
A functional limit theorem for additive functionals
Thibaud Taillefumier, Gordan Zitkovic
We study a general limiting framework for the convergence of sequences of additive functionals of diffusions to Lévy subordinators, and provide explicit sufficient conditions that…
Global solutions with infinitely many blowups in a mean-field neural network
Lorenzo Sadun, Thibaud Taillefumier
We recently introduced idealized mean-field models for networks of integrate-and-fire neurons with impulse-like interactions -- the so-called delayed Poissonian mean-field models.…
Characterization of blowups via time change in a mean-field neural network
Thibaud Taillefumier, Phillip Whitman
Idealized networks of integrate-and-fire neurons with impulse-like interactions obey McKean-Vlasov diffusion equations in the mean-field limit. These equations are prone to blowups…
Replica-Mean-Field Limits of Fragmentation-Interaction-Aggregation Processes
François Baccelli, Michel Davydov, Thibaud Taillefumier
Network dynamics with point-process-based interactions are of paramount modeling interest. Unfortunately, most relevant dynamics involve complex graphs of interactions for which an…
The Pair-Replica-Mean-Field Limit for Intensity-based Neural Networks
François Baccelli, Thibaud Taillefumier
Replica-mean-field models have been proposed to decipher the activity of neural networks via a multiply-and-conquer approach. In this approach, one considers limit networks made of…
Multi-Resolution Schauder Approach to Multidimensional Gauss-Markov Processes
Thibaud Taillefumier, Jonathan Touboul
The study of multidimensional stochastic processes involves complex computations in intricate functional spaces. In particular, the diffusion processes, which include the practical…