On the Almost Sure Convergence Rate for A Series Expansion of Fractional Brownian Motion
On the Almost Sure Convergence Rate for A Series Expansion of Fractional Brownian Motion
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DOI：
10.1109/wsc40007.2019.9004731
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发表时间：
2019-12
期刊：
影响因子：
--
通讯作者：
Yi Chen;Jing Dong
中科院分区：
文献类型：
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作者：
Yi Chen;Jing Dong
分数布朗运动（fBM）及其相关过程被广泛应用于金融建模中，以捕捉波动率的复杂依赖结构。本文分析了Dzhaparidze和货车Zanten在2004年提出的fBM的无穷级数表示，并建立了该级数表示的几乎处处收敛速度.该速率也被证明是最佳的。然后，我们展示了如何强收敛速度的结果可以应用于构建仿真算法的路径误差保证。
Fractional Brownian motions (fBM) and related processes are widely used in financial modeling to capture the complicated dependence structure of the volatility. In this paper, we analyze an infinite series representation of fBM proposed in (Dzhaparidze and Van Zanten 2004) and establish an almost sure convergence rate of the series representation. The rate is also shown to be optimal. We then demonstrate how the strong convergence rate result can be applied to construct simulation algorithms with path-by-path error guarantees.