Strong rate of convergence for the Euler-Maruyama approximation of SDEs with Hölder continuous drift coefficient

DOI10.1016/J.SPA.2016.11.008zbMATH Open1367.60090arXiv1508.07513OpenAlexW2964246490MaRDI QIDQ2360241

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Publication date: 30 June 2017

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Abstract: In this paper, we consider a numerical approximation of the stochastic differential equation (SDE) ${\displaystyle }$X_{t}=x_{0}+ int_{0}^{t} b(s, X_{s}) mathrm{d}s + L_{t},~x_{0} in mathbb{R}^{d},~t in [0,T],${\displaystyle }$ where the drift coefficient $b:[0,T]imesmathbb{R}^{d}omathbb{R}^d$ is H"older continuous in both time and space variables and the noise $L=(L_t{)}_{0leqtleqT}$ is a $d$-dimensional L'evy process. We provide the rate of convergence for the Euler-Maruyama approximation when $L$ is a Wiener process or a truncated symmetric $alpha$-stable process with $alphain(1,2)$. Our technique is based on the regularity of the solution to the associated Kolmogorov equation.

Full work available at URL: https://arxiv.org/abs/1508.07513

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