论文标题
布朗分数运动：局部连续性模量，精制的几乎确定的上限和第一次退出时间从单方面屏障
Fractional Brownian Motion: Local Modulus of Continuity with Refined Almost Sure Upper Bound and First Exit Time from One-sided Barrier
论文作者
论文摘要
基于最佳速率小波序列表示，我们得出了连续性结果的局部模量，并且几乎确定了分数布朗运动的上限。 \ sloppy $ \ mathcal o_ {a.s。} \ big（|该结果填补了分数布朗运动的迭代对数定律的空白，其中缺少上界随机乘数的矩信息。通过这种增强的上限和一些关于分数布朗运动最大分布的新结果，我们获得了一个新的且精致的渐近估计，用于上尾的概率，用于$ t \ to+fty hyfty $，用于首先从正时$ t $ $ t $中退出正值的屏障。
Based on an optimal rate wavelet series representation, we derive a local modulus of continuity result with a refined almost sure upper bound for fractional Brownian motion. \sloppy The obtained upper bound of the small fractional Brownian increments is of order $\mathcal O_{a.s.}\big(|h|^H\sqrt{\log\log |h|^{-1}}\big)$ as $|h|\to0$, and an upper bound of its $p$th moment is provided, for any $p>0$. This result fills the gap of the law of iterated logarithm for fractional Brownian motion, where the moments' information of the random multiplier in the upper bound is missing. With this enhanced upper bound and some new results on the distribution of the maximum of fractional Brownian motion, we obtain a new and refined asymptotic estimate of the upper-tail probability for a fractional Brownian motion to first exit from a positive-valued barrier over time $T$, as $T\to+\infty$.
