  In previous work, we introduced a method for determining convergence rates
for integration methods for the kinetic Langevin equation for
$M$-$\nabla$Lipschitz $m$-log-concave densities [arXiv:2302.10684, 2023]. In
this article, we exploit this method to treat several additional schemes
including the method of Brunger, Brooks and Karplus (BBK) and stochastic
position/velocity Verlet. We introduce a randomized midpoint scheme for kinetic
Langevin dynamics, inspired by the recent scheme of Bou-Rabee and Marsden
[arXiv:2211.11003, 2022]. We also extend our approach to stochastic gradient
variants of these schemes under minimal extra assumptions. We provide
convergence rates of $\mathcal{O}(m/M)$, with explicit stepsize restriction,
which are of the same order as the stability thresholds for Gaussian targets
and are valid for a large interval of the friction parameter. We compare the
contraction rate estimates of many kinetic Langevin integrators from molecular
dynamics and machine learning. Finally we present numerical experiments for a
Bayesian logistic regression example.
