77 citations · 161 across the 14 of their papers we have counts for
19 papers
Freidlin-Wentzell collision-laws between self-stabilizing diffusions
Jean-François Jabir, Julian Tugaut
The present work investigates the asymptotic behaviours at the zero-noise limit of the first near collision-time and first near collision-location between a pair of independent …
Multi-species McKean-Vlasov dynamics in non-convex landscapes
Manh Hong Duong, Grigorios A. Pavliotis, Julian Tugaut
In this paper, we study multi-species stochastic interacting particle systems and their mean-field McKean-Vlasov partial differential equations (PDEs) in non-convex landscapes. Und…
Measure-dependent non-linear diffusions with superlinear drifts: asymptotic behaviour of the first exit-times
Ashot Aleksian, Julian Tugaut
In this paper, we study McKean-Vlasov SDE living in in the reversible case without assuming any type of convexity assumptions for confinement or interaction potentia…
Exit-problem for a class of non-Markov processes with path dependency
Ashot Aleksian, Aline Kurtzmann, Julian Tugaut
We study the exit-time of a self-interacting diffusion from an open domain . In particular, we consider the equation $d{X_t} = - \left( \nabla V(X_t) + \fra…
Self-interacting diffusions: long-time behaviour and exit-problem in the convex case
Ashot Aleksian, Pierre del Moral, Aline Kurtzmann +1
We study a class of time-inhomogeneous diffusion: the self-interacting one. We show a convergence result with a rate of convergence that does not depend on the diffusion coefficien…
A Kramers' type law for the first collision-time of two self-stabilizing diffusions and of their particle approximations
Jean-Francois Jabir, Julian Tugaut
The present work investigates the asymptotic behaviors, at the zero-noise limit, of the first collision-time and first collision-location related to a pair of self-stabilizing diff…
Granular media equation with double-well external landscape: limiting steady state
Julian Tugaut
In this paper, we give a simple condition on the initial state of the granular media equation which ensures that the limit as the time goes to infinity is the unique steady state w…
On the exit-problem for self-interacting diffusions
Ashot Aleksian, Pierre Del Moral, Aline Kurtzmann +1
We study the exit-time from a domain of a self-interacting diffusion, where the Brownian motion is replaced by for a constant . The first part of this work consists in sh…
Reducing exit-times of diffusions with repulsive interactions
Paul-Eric Chaudru de Raynal, Manh Hong Duong, Pierre Monmarché +2
In this work we prove a Kramers' type law for the low-temperature behavior of the exit-times from a metastable state for a class of self-interacting nonlinear diffusion processes.…
Large Deviations and Exit-times for reflected McKean-Vlasov equations with self-stabilizing terms and superlinear drifts
Daniel Adams, Gonçalo dos Reis, Romain Ravaille +2
We study a class of reflected McKean-Vlasov diffusions over a convex domain with self-stabilizing coefficients. This includes coefficients that do not satisfy the classical Wassers…
Coupled McKean-Vlasov diffusions: wellposedness, propagation of chaos and invariant measures
Manh Hong Duong, Julian Tugaut
In this paper, we study a two-species model in the form of a coupled system of nonlinear stochastic differential equations (SDEs) that arises from a variety of applications such as…
The Vlasov-Fokker-Planck equation in non-convex landscapes: convergence to equilibrium
Manh Hong Duong, Julian Tugaut
In this paper, we study the long-time behaviour of solutions to the Vlasov-Fokker-Planck equation where the confining potential is non-convex. This is a nonlocal nonlinear partial…
Freidlin-Wentzell LDP in path space for McKean-Vlasov equations and the Functional Iterated Logarithm Law
Goncalo Dos Reis, William Salkeld, Julian Tugaut
We show two Freidlin-Wentzell type Large Deviations Principles (LDP) in path space topologies (uniform and Hölder) for the solution process of McKean-Vlasov Stochastic Differential…
On the stability and the uniform propagation of chaos of a class of Extended Ensemble Kalman-Bucy filters
Pierre Del Moral, Aline Kurtzmann, Julian Tugaut
This article is concerned with the exponential stability and the uniform propagation of chaos properties of a class of Extended Ensemble Kalman-Bucy filters with respect to the tim…
On the Stability and the Exponential Concentration of Extended Kalman-Bucy filters
Pierre Del Moral, Aline Kurtzmann, Julian Tugaut
The exponential stability and the concentration properties of a class of extended Kalman-Bucy filters are analyzed. New estimation concentration inequalities around partially obser…
On the stability and the uniform propagation of chaos properties of Ensemble Kalman-Bucy filters
Pierre Del Moral, Julian Tugaut
The Ensemble Kalman filter is a sophisticated and powerful data assimilation method for filtering high dimensional problems arising in fluid mechanics and geophysical sciences. Thi…
Stationary solutions of the Vlasov-Fokker-Planck equation: existence, characterization and phase-transition
Manh Hong Duong, Julian Tugaut
In this paper, we study the set of stationary solutions of the Vlasov-Fokker-Planck (VFP) equation. This equation describes the time evolution of the probability distribution of a…
Mean-field limit versus small-noise limit for some interacting particle systems
Samuel Herrmann, Julian Tugaut
In the nonlinear diffusion framework, stochastic processes of McKean-Vlasov type play an important role. In some cases they correspond to processes attracted by their own probabili…
Convergence to the equilibria for self-stabilizing processes in double-well landscape
Julian Tugaut
We investigate the convergence of McKean-Vlasov diffusions in a nonconvex landscape. These processes are linked to nonlinear partial differential equations. According to our previo…