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. This allows us to study in a unified way a number of different integrators proposed in the literature for the overdamped and underdamped Langevin dynamics. In addition, we analyze a novel splitting method for the underdamped Langevin dynamics which only requires one gradient evaluation per time step. Under an additional smoothness assumption on a d
--dimensional strongly log-concave distribution with condition number κ
, the algorithm is shown to produce with an O(κ5/4d1/4ϵ−1/2)
complexity samples from a distribution that, in Wasserstein distance, is at most ϵ>0
away from the target distribution
