具有不连续漂移和退化扩散系数的多维随机微分方程的欧拉-丸山方法的收敛性
Convergence of the Euler-Maruyama method for multidimensional SDEs with discontinuous drift and degenerate diffusion coefficient.
作者信息
Leobacher Gunther, Szölgyenyi Michaela
机构信息
1Institute of Mathematics and Scientific Computing, University of Graz, Heinrichstraße 36, 8010 Graz, Austria.
2Institute for Statistics and Mathematics, Vienna University of Economics and Business (WU), Welthandelsplatz 1, 1020 Vienna, Austria.
出版信息
Numer Math (Heidelb). 2018;138(1):219-239. doi: 10.1007/s00211-017-0903-9. Epub 2017 Jul 20.
We prove strong convergence of order [Formula: see text] for arbitrarily small [Formula: see text] 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.
我们证明了对于具有不连续漂移和退化扩散系数的多维随机微分方程（SDEs），当步长任意小为[公式：见原文]时，欧拉 - 丸山方法的[公式：见原文]阶强收敛性。证明基于估计欧拉 - 丸山格式与另一种数值方法之间的差异，该数值方法是通过将欧拉 - 丸山格式应用于我们旨在求解的随机微分方程的一种变换而构建的。
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