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Статья

The tamed unadjusted Langevin algorithm

Moulines E., Brosse N., Durmus A., Sabanis S.

In this article, we consider the problem of sampling from a probability measure π having a density on R d proportional to x↦ e− U (x). The Euler discretization of the Langevin stochastic differential equation (SDE) is known to be unstable, when the potential U is superlinear. Based on previous works on the taming of superlinear drift coefficients for SDEs, we introduce the Tamed Unadjusted Langevin Algorithm (TULA) and obtain non-asymptotic bounds in V-total variation norm and Wasserstein distance of order 2 between the iterates of TULA and π, as well as weak error bounds. Numerical experiments are presented which support our findings.