# On the regularisation of the noise for the Euler-Maruyama scheme with irregular drift

@article{Dareiotis2018OnTR, title={On the regularisation of the noise for the Euler-Maruyama scheme with irregular drift}, author={Konstantinos Dareiotis and M'at'e Gerencs'er}, journal={arXiv: Probability}, year={2018} }

The strong rate of convergence of the Euler-Maruyama scheme for nondegenerate SDEs with irregular drift coefficients is considered. In the case of $\alpha$-Holder drift in recent literature the rate $\alpha/2$ was proved in many related situations. By exploiting the regularising effect of the noise more efficiently, we show that the rate is in fact arbitrarily close to $1/2$ for all $\alpha>0$. The result extends to Dini continuous coefficients, while in $d=1$ also to a class of everywhere…

## 16 Citations

The Euler–Maruyama scheme for SDEs with irregular drift: convergence rates via reduction to a quadrature problem

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- 2020

We study the strong convergence order of the Euler-Maruyama scheme for scalar stochastic differential equations with additive noise and irregular drift. We provide a general framework for the error…

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In the past decade, an intensive study of strong approximation of stochastic differential equations (SDEs) with a drift coefficient that has discontinuities in space has begun. In the majority of…

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- Computer Science, MathematicsArXiv
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This is the first paper to study (and implement) numerical solutions of SDEs whose drift cannot be expressed as a function of the state and the approximating process, obtained by the scheme, converges in law to the (virtual) solution of the SDE in a general multi-dimensional setting.

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In this paper, we investigate the weak convergence rate of Euler-Maruyama’s approximation for stochastic differential equations with low regular drifts. Explicit weak convergence rates are presented…

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It is shown 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 and error estimates are derived.

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- Computer Science, MathematicsArXiv
- 2021

This work considers a generic and explicit tamed Euler–Maruyama scheme for multidimensional time-inhomogeneous stochastic equations with multiplicative Brownian noise with strong rate of convergence in terms of the approximation error of the drift in a suitable and possibly very weak topology.

Convergence Rate of the Euler-Maruyama Scheme Applied to Diffusion Processes with L Q -- L $\rho$ Drift Coefficient and Additive Noise

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- 2021

BY BENJAMIN JOURDAIN1 AND STÉPHANE MENOZZI2,* 1Cermics, Ecole des Ponts, INRIA, Marne-la-Vallée, France, benjamin.jourdain@enpc.fr 2Laboratoire de Modélisation Mathématique d’Evry (LaMME), Université…

Existence of strong solutions for It\^o's stochastic equations via approximations. Revisited

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Given strong uniqueness for an Itô’s stochastic equation, we prove that its solution can be constructed on “any” probability space by using, for example, Euler’s polygonal approximations. Stochastic…

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An overview of the work for the case that the drift coefficient is potentially discontinuous complemented by other important results in this area is given.

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