Strong rate of convergence for the Euler-Maruyama approximation of SDEs with H\"older continuous drift coefficient
Strong rate of convergence for the Euler-Maruyama approximation of SDEs with H\"older continuous drift coefficient
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DOI：
10.1016/j.spa.2016.11.008
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发表时间：
2015-08
期刊：
影响因子：
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通讯作者：
O. M. Pamen;Daichi Taguchi
中科院分区：
文献类型：
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作者：
O. M. Pamen;Daichi Taguchi
本文考虑随机微分方程（SDE） X t= X 0+∫0 t b (s, X s) d s+ L t, X 0∈R d, t∈[0，t]的一个数值逼近，其中漂移系数b:[0， t]× R d→R d在时间和空间变量上都是Hölder连续的，噪声L=(L t) 0≤t≤t是一个d维l<s:1> <s:1>过程。给出了当L是Wiener过程或α∈(1,2)的截断对称α-稳定过程时Euler-Maruyama近似的收敛速率。我们的技术是基于相关Kolmogorov方程解的规律性。
In this paper, we consider a numerical approximation of the stochastic differential equation (SDE) X t= x 0+∫ 0 t b (s, X s) d s+ L t, x 0∈ R d, t∈[0, T], where the drift coefficient b:[0, T]× R d→ R d is Hölder continuous in both time and space variables and the noise L=(L t) 0≤ t≤ T is a d-dimensional Lévy process. We provide the rate of convergence for the Euler–Maruyama approximation when L is a Wiener process or a truncated symmetric α-stable process with α∈(1, 2). Our technique is based on the regularity of the solution to the associated Kolmogorov equation.