This book is a substantially revised and expanded edition reflecting major developments in
stochastic numerics since the 1st edition [314] was published in 2004. The new topics …

Bridging the gap between constant step size stochastic gradient descent and Markov chains
Page 1 The Annals of Statistics 2020, Vol. 48, No. 3, 1348–1382 https://doi.org/10.1214/19-AOS1850 …

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

Inexact Markov chain Monte Carlo methods rely on Markov chains that do not exactly
preserve the target distribution. Examples include the unadjusted Langevin algorithm (ULA) …

Invariant Measures for Stochastic Nonlinear Schrödinger Equations | SpringerLink Skip to main
content Advertisement Springer Nature Link Account Menu Find a journal Publish with us Track …

As numerous modern challenges in scientific questions, industrial needs, and societal
requirements emerge, the demand for designing numerical methods to solve tremendously …

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

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 …

A new characterization of sufficient conditions for the Lie--Trotter splitting to capture the
numerical invariant measure of nonlinear ergodic Langevin dynamics up to an arbitrary …

We present dimension-free convergence and discretization error bounds for the unadjusted
Hamiltonian Monte Carlo algorithm applied to high-dimensional probability distributions of …