The Tamed Unadjusted Langevin Algorithm

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