3 citations · 6 across the 6 of their papers we have counts for
9 papers · 1 filter
A Lyapunov-tamed Euler method for singular SDEs
Tim Johnston, Pierre Monmarché
Many applications, such as systems of interacting particles in physics, require the simulation of diffusion processes with singular coefficients. Standard Euler schemes are then no…
Some remarks on the effect of the Random Batch Method on phase transition
Arnaud Guillin, Pierre Le Bris, Pierre Monmarché
In this article, we focus on two toy models : the Curie-Weiss model and the system of particles in linear interactions in a double well confining potential. Both models, which…
On systems of particles in singular repulsive interaction in dimension one : log and Riesz gas
Arnaud Guillin, Pierre Le Bris, Pierre Monmarché
In this article, we prove the first quantitative uniform in time propagation of chaos for a class of systems of particles in singular repulsive interaction in dimension one that co…
Convergence rates for the Vlasov-Fokker-Planck equation and uniform in time propagation of chaos in non convex cases
Arnaud Guillin, Pierre Le Bris, Pierre Monmarché
We prove the existence of a contraction rate for Vlasov-Fokker-Planck equation in Wasserstein distance, provided the interaction potential is (locally) Lipschitz continuous and the…
Discrete sticky couplings of functional autoregressive processes
Alain Durmus, Andreas Eberle, Aurélien Enfroy +2
In this paper, we provide bounds in Wasserstein and total variation distances between the distributions of the successive iterates of two functional autoregressive processes with i…
Piecewise Deterministic Markov Processes and their invariant measures
Alain Durmus, Arnaud Guillin, Pierre Monmarché
Piecewise Deterministic Markov Processes (PDMPs) are studied in a general framework. First, different constructions are proven to be equivalent. Second, we introduce a coupling bet…
Geometric ergodicity of the bouncy particle sampler
Alain Durmus, Arnaud Guillin, Pierre Monmarché
The Bouncy Particle Sampler (BPS) is a Monte Carlo Markov Chain algorithm to sample from a target density known up to a multiplicative constant. This method is based on a kinetic p…
Entropic multipliers method for langevin diffusion and weighted log sobolev inequalities
Patrick Cattiaux, Arnaud Guillin, Pierre Monmarché +1
In his work about hypocercivity, Villani [18] considers in particular convergence to equilibrium for the kinetic Langevin process. While his convergence results in L 2 are given in…
Optimal linear drift for the speed of convergence of an hypoelliptic diffusion
Arnaud Guillin, Pierre Monmarché
Among all generalized Ornstein-Uhlenbeck processes which sample the same invariant measure and for which the same amount of randomness (a -dimensional Brownian motion) is inject…