Error estimates of the backward Euler–Maruyama method for multi-valued stochastic differential equations
Journal article, 2021

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 et al. (Commun Pure Appl Math 53(5):525–589, 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.

Stochastic inclusion equation

Hölder continuous drift

Strong convergence

Backward Euler–Maruyama method

Discontinuous drift

Stochastic gradient flow

Multi-valued stochastic differential equation


Monika Eisenmann

Lund University

Mihaly Kovacs

Pázmány Péter Catholic University

Raphael Kruse

Martin-Luther-Universität Halle-Wittenberg

Stig Larsson

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

BIT (Copenhagen)

0006-3835 (ISSN)

Vol. In Press

Subject Categories

Computational Mathematics

Probability Theory and Statistics

Mathematical Analysis



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