Error estimates of the backward Euler-Maruyama method for multi-valued stochastic differential equations
Preprint, 2019

In this paper, we derive error estimates of the backward Euler-Maruyama method applied to multi-valued stochastic differential equations. An important example of such an equation is a stochastic gradient flow whose associated potential is not continuously differentiable, but assumed to be convex. We show that the backward Euler-Maruyama method is well-defined and convergent of order at least 1/4 with respect to the root-mean-square norm. Our error analysis relies on techniques for deterministic problems developed in [Nochetto, Savaré, and Verdi, Comm.\ Pure Appl.\ Math., 2000]. We verify that our setting applies to an overdamped Langevin equation with a discontinuous gradient and to a spatially semi-discrete approximation of the stochastic p-Laplace equation.

multi-valued stochastic differential equation

stochastic gradient flow

backward Euler-Maruyama method

Hölder continuous drift

discontinuous drift

strong convergence


Monika Eisenmann

Mihaly Kovacs

Raphael Kruse

Stig Larsson

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik



Sannolikhetsteori och statistik

Matematisk analys


Grundläggande vetenskaper

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