Strong convergence for Euler-Maruyama and Milstein schemes with asymptotic method
Strong convergence for Euler-Maruyama and Milstein schemes with asymptotic method
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Euler-Maruyama 和 Milstein 格式渐进方法的强收敛性
DOI：
10.1142/s0219024914500149
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发表时间：
2014
影响因子：
0.5
通讯作者：
T. Yamada
中科院分区：
文献类型：
--
作者：
H. Tanaka;T. Yamada
受 Takahashi 和 Yoshida (2005) 论文中弱收敛结果的启发，我们展示了应用于扰动随机微分方程的加速 Euler-Maruyama 格式的强收敛性。具有相同加速度的米尔斯坦方案也作为扩展结果进行了讨论。理论结果可用于分析M.B.最初开发的多级蒙特卡罗方法。贾尔斯.为了证实该方案的有效性，提出了随机波动率的随机 alpha-beta-rho (SABR) 模型的几个数值实验。
Motivated by weak convergence results in the paper of Takahashi & Yoshida (2005), we show strong convergence for an accelerated Euler–Maruyama scheme applied to perturbed stochastic differential equations. The Milstein scheme with the same acceleration is also discussed as an extended result. The theoretical results can be applied to analyze the multi-level Monte Carlo method originally developed by M.B. Giles. Several numerical experiments for the stochastic alpha-beta-rho (SABR) model of stochastic volatility are presented in order to confirm the efficiency of the schemes.