The paper titled "Fractional Brownian Motion: Local Modulus of Continuity with Refined Almost Sure Upper Bound and First Exit Time from One-sided Barrier" is found at https://arxiv.org/abs/2208.03327. The main formula derived in the paper is an upper bound for the probability of a fractional Brownian motion (fBm) exceeding a given level at a given time. Specifically, the authors derive the following upper bound for the probability of an fBm with Hurst parameter H exceeding the level 1 at time t: P sup_{0<=s<=t} B_H(s) > 1 <= T^{-(1-H)} (log T)^{(1/H-1)} (log^2 T)^{3/(2H)} (log^3 T)^{1/H} (log^4 N)^{1/(2H)} Here, B_H(t) denotes the fractional Brownian motion with Hurst parameter H, and the probability is taken over all possible paths of the fBm. The authors also provide an upper bound for the first exit time of an fBm from a one-sided barrier, which involves a similar expression involving logarithmic factors.
There appears to be a typo in your URL. The correct link is: https://arxiv.org/abs/2207.10247?context=math