Wasserstein distance estimates for the distributions of numerical approximations to ergodic stochastic differential equations

no code implementations • 26 Apr 2021 • J. M. Sanz-Serna, Konstantinos C. Zygalakis

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 distribution of its numerical approximation in the strongly log-concave case.

The connections between Lyapunov functions for some optimization algorithms and differential equations

no code implementations • 1 Sep 2020 • J. M. Sanz-Serna, Konstantinos C. Zygalakis

In the appropriate limit, this family of methods may be seen as a discretization of a family of second-order ordinary differential equations for which we construct(continuous) Lyapunov functions by means of the LMI framework.