论文标题
$ l^p $统一随机步行类型的近似，用于赫斯特·恩斯特的分数布朗运动$ 0 <h <\ frac {1} {2} {2} $
$L^p$ uniform random walk-type approximation for fractional Brownian motion with Hurst exponent $0 < H < \frac{1}{2}$
论文作者
论文摘要
在本说明中，我们证明了$ l^p $统一的近似布朗尼运动的近似值，赫斯特指数$ 0 <h <\ frac {1} {2} $，通过在给定的布朗尼运动中陷入的连续时间随机步行家族。近似是通过标准布朗运动的路径布朗运动的路径表示。对于随机步行家族的跳跃大小的任意选择$ε_k$，近似方案的收敛速度为$ O（ε_k^{p（1-2λ）+ 2（δ-1）}）$，每当$ \ \ max \ max \ max \ max \ frac {0,1- \ frac {ph} \ big（\ frac {1-h} {2}，\ frac {1} {2} + \ frac {δ-1} {p} {p} {p} \ big）$。
In this note, we prove an $L^p$ uniform approximation of the fractional Brownian motion with Hurst exponent $0 < H < \frac{1}{2}$ by means of a family of continuous-time random walks imbedded on a given Brownian motion. The approximation is constructed via a pathwise representation of the fractional Brownian motion in terms of a standard Brownian motion. For an arbitrary choice $ε_k$ for the size of the jumps of the family of random walks, the rate of convergence of the approximation scheme is $O(ε_k^{p(1-2λ)+ 2(δ-1)})$ whenever $\max\{0,1-\frac{pH}{2}\}< δ< 1$, $λ\in \big(\frac{1-H}{2}, \frac{1}{2} + \frac{δ-1}{p}\big)$.
