论文标题
由加性粗糙分数噪声驱动的SDE的EULER方案的强收敛率
Strong convergence rate of the Euler scheme for SDEs driven by additive rough fractional noises
论文作者
论文摘要
研究了由加性分数布朗尼动作驱动的SDE的EULER方案的强收敛速率，其中分数Brownian运动具有Hurst参数$ H \ in（\ frac13，\ frac12）$，并且不需要漂移系数。 Malliavin微积分，粗糙的路径理论和$ 2 $ d的年轻积分被用来克服因小数布朗运动的低规律性和漂移系数的无限性而造成的困难。事实证明，Euler计划的订单$ 2H $，对于线性案例，漂移系数已将衍生品的限制为第三次，并且具有强订单$ h+\ frac12 $。提出数值模拟以支持理论结果。
The strong convergence rate of the Euler scheme for SDEs driven by additive fractional Brownian motions is studied, where the fractional Brownian motion has Hurst parameter $H\in(\frac13,\frac12)$ and the drift coefficient is not required to be bounded. The Malliavin calculus, the rough path theory and the $2$D Young integral are utilized to overcome the difficulties caused by the low regularity of the fractional Brownian motion and the unboundedness of the drift coefficient. The Euler scheme is proved to have strong order $2H$ for the case that the drift coefficient has bounded derivatives up to order three and have strong order $H+\frac12$ for linear cases. Numerical simulations are presented to support the theoretical results.
