On the performance of the Euler-Maruyama scheme for SDEs with discontinuous drift coefficient
type: Item
instance of: scholarly article
title: On the performance of the Euler-Maruyama scheme for SDEs with discontinuous drift coefficient
zbMATH Open document ID: 1494.65006
DOI: 10.1214/19-AIHP997
author: Thomas Müller-Gronbach
author: Larisa Yaroslavtseva
published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques
publication date: 2020-05-13T00:00:00Z
full work available at URL: https://arxiv.org/abs/1809.08423
full work available at URL: https://projecteuclid.org/euclid.aihp/1584345633
review text: The authors consider the autonomous differential equation \[ \begin{aligned} dX_t & = \mu(X_t)dt + \sigma(X_t)dW_t, \quad t \in [0,1] \\ X_0 & = x_0 \end{aligned} \] They study the performance of the Euler scheme in the case where the drift coefficient has infinitely many discontinuities. They show the following estimate \[ (\mathbb{E}[\|X-X_n\|_q^p])^{1/p} \leq \begin{cases} c/ \sqrt{n}, & \text{ if } q < \infty,\\ c \sqrt{\ln (n+1)}/\sqrt{n}, & \text{ if } q = \infty. \end{cases} \]
reviewed by: Nikolaos Halidias
Mathematics Subject Classification ID: 65C30
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60H35
zbMATH DE Number: 7199893
zbMATH Keywords: stochastic differential equations
zbMATH Keywords: discontinuous drift coefficient
zbMATH Keywords: strong approximation
zbMATH Keywords: Euler-Maruyama scheme
MaRDI profile type: Publication
arXiv ID: 1809.08423
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OpenAlex ID: W3010883102
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