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Convergence of the Euler–Maruyama method for multidimensional SDEs with discontinuous drift and degenerate diffusion coefficient
Numerische Mathematik ( IF 2.1 ) Pub Date : 2017-07-20 , DOI: 10.1007/s00211-017-0903-9
Gunther Leobacher 1 , Michaela Szölgyenyi 2
Affiliation  

We prove strong convergence of order $$1/4-\epsilon $$1/4-ϵ for arbitrarily small $$\epsilon >0$$ϵ>0 of the Euler–Maruyama method for multidimensional stochastic differential equations (SDEs) with discontinuous drift and degenerate diffusion coefficient. The proof is based on estimating the difference between the Euler–Maruyama scheme and another numerical method, which is constructed by applying the Euler–Maruyama scheme to a transformation of the SDE we aim to solve.

中文翻译:

具有不连续漂移和简并扩散系数的多维 SDE 的 Euler-Maruyama 方法的收敛性

我们证明了具有不连续漂移的多维随机微分方程 (SDE) 的 Euler-Maruyama 方法的任意小 $$\epsilon >0$$ϵ>0 阶 $$1/4-\epsilon $$1/4-ϵ 的强收敛性和简并扩散系数。该证明基于估计 Euler-Maruyama 格式与另一种数值方法之间的差异,该方法是通过将 Euler-Maruyama 格式应用于我们要解决的 SDE 的变换而构建的。
更新日期:2017-07-20
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