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Journal Articles Stochastic Processes and their Applications Year : 2018

The Tamed Unadjusted Langevin Algorithm

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Abstract

In this article, we consider the problem of sampling from a probability measure π having a density on R d known up to a normalizing constant, $x → e −U (x) / R d e −U (y) dy$. The Euler discretization of the Langevin stochastic differential equation (SDE) is known to be unstable in a precise sense, when the potential U is superlinear, i.e. lim inf $x→+∞ U (x) / x = +∞$. 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.
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Dates and versions

hal-01648667 , version 1 (27-11-2017)

Identifiers

Cite

Nicolas Brosse, Alain Durmus, Éric Moulines, Sotirios Sabanis. The Tamed Unadjusted Langevin Algorithm. Stochastic Processes and their Applications, 2018, ⟨10.1016/j.spa.2018.10.002⟩. ⟨hal-01648667⟩
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