论文标题
使用耦合的分数布朗运动的预期至上的下限
Lower bound for the expected supremum of fractional Brownian motion using coupling
论文作者
论文摘要
我们为（in）有限的时间范围内（0,1）$ in（0,1）$ in（0,1）$ in（0,1）$ in（0,1）$ hurst index $ h \ in（in）有限的时间范围，我们得出了一个新的理论下限。广泛的仿真实验表明，我们的下边界的表现优于蒙特卡洛估计值，基于$ h \ in（0，\ tfrac {1} {2}）$的非常密集的网格。此外，我们得出了线性分数布朗运动的Paley-Wiener-Zygmund表示，并在Bisewski，dębicki＆Rolski（20221）的最新工作中为预期的超级衍生物提供了明确的表达。
We derive a new theoretical lower bound for the expected supremum of drifted fractional Brownian motion with Hurst index $H\in(0,1)$ over (in)finite time horizon. Extensive simulation experiments indicate that our lower bound outperforms the Monte Carlo estimates based on very dense grids for $H\in(0,\tfrac{1}{2})$. Additionally, we derive the Paley-Wiener-Zygmund representation of a Linear Fractional Brownian motion and give an explicit expression for the derivative of the expected supremum at $H=\tfrac{1}{2}$ in the sense of recent work by Bisewski, Dębicki & Rolski (2021).
