In this paper we describe a general framework for deriving modified equations for stochastic
differential equations (SDEs) with respect to weak convergence. Modified equations are …

In this manuscript we study the properties of a family of a second-order differential equations
with damping, its discretizations, and their connections with accelerated optimization …

Applying standard Markov chain Monte Carlo (MCMC) algorithms to large data sets is
computationally infeasible. The recently proposed stochastic gradient Langevin dynamics (SGLD) …

We present a framework that allows for the non-asymptotic study of the 2-Wasserstein distance
between the invariant distribution of an ergodic stochastic differential equation and the …

A class of Brownian dynamics algorithms for stochastic reaction-diffusion models which
include reversible bimolecular reactions is presented and analyzed. The method is a …

We introduce new sufficient conditions for a numerical method to approximate with high order
of accuracy the invariant measure of an ergodic system of stochastic differential equations, …

We present a highly efficient proximal Markov chain Monte Carlo methodology to perform
Bayesian computation in imaging problems. Similarly to previous proximal Monte Carlo …

The 3DVAR filter is prototypical of methods used to combine observed data with a dynamical
system, online, in order to improve estimation of the state of the system. Such methods are …

Classification of high dimensional data finds wide-ranging applications. In many of these
applications equipping the resulting classification with a measure of uncertainty may be as …

Inspired by recent advances in the theory of modified differential equations, we propose a
new methodology for constructing numerical integrators with high weak order for the time …