The tamed unadjusted Langevin algorithm

Nicolas Brosse, Alain Durmus, Éric Moulines and Sotirios Sabanis

Stochastic Processes and their Applications, 2019, vol. 129, issue 10, 3638-3663

Abstract: In this article, we consider the problem of sampling from a probability measure π having a density on Rd 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.

Keywords: Tamed unadjusted Langevin algorithm; Markov chain Monte Carlo; Total variation distance; Wasserstein distance (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:129:y:2019:i:10:p:3638-3663

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DOI: 10.1016/j.spa.2018.10.002

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