4 papers
Long time behavior in locally activated random walks
Nicolas Meunier, Clément Mouhot, Raphaël Roux
We consider a 1-dimensional Brownian motion whose diffusion coefficient varies when it crosses the origin. We study the long time behavior and we establish different regimes, depen…
Computation of sensitivities for the invariant measure of a parameter dependent diffusion
Roland Assaraf, Benjamin Jourdain, Tony Lelièvre +1
We consider the solution to a stochastic differential equation with a drift function which depends smoothly on some real parameter , and admitting a unique invariant measure for…
Convergence of a stochastic particle approximation for fractional scalar conservation laws
Benjamin Jourdain, Raphaël Roux
We give a probabilistic numerical method for solving a partial differential equation with fractional diffusion and nonlinear drift. The probabilistic interpretation of this equatio…
Existence, uniqueness and convergence of a particle approximation for the Adaptive Biasing Force process
Benjamin Jourdain, Tony Lelievre, Raphaël Roux
We prove existence and uniqueness for some nonlinear stochastic differential equation used in molecular dynamics, whose nonlinearity comes from a conditional expectation term. We a…