Unadjusted Langevin algorithm with multiplicative noise: Total variation and Wasserstein bounds

In this paper, we focus on nonasymptotic bounds related to the Euler scheme of an ergodic diffusion with a possibly multiplicative term (nonconstant coefficient). More precisely, objective paper is control distance standard decreasing step (usually called unadjusted Langevin algorithm in Monte Carlo literature) invariant distribution such diffusion. appropriate Lyapunov setting and under uniform ellipticity assumptions coefficient, establish (or improve) for total variation L1-Wasserstein distances both additive frameworks. These rely weak error expansions using stochastic analysis adapted setting.