For sampling from a log-concave density, we study implicit integrators
resulting from θ-method discretization of the overdamped Langevin
diffusion stochastic differential equation. Theoretical and algorithmic
properties of the resulting sampling methods for θ∈[0,1] and a
range of step sizes are established. Our results generalize and extend prior
works in several directions. In particular, for θ≥1/2, we prove
geometric ergodicity and stability of the resulting methods for all step sizes.
We show that obtaining subsequent samples amounts to solving a strongly-convex
optimization problem, which is readily achievable using one of numerous
existing methods. Numerical examples supporting our theoretical analysis are
also presented