  The three arcsine laws for Brownian motion are a cornerstone of extreme-value
statistics. For a Brownian $B_t$ starting from the origin, and evolving during
time $T$, one considers the following three observables: (i) the duration $t_+$
the process is positive, (ii) the time $t_{\rm last}$ the process last visits
the origin, and (iii) the time $t_{\rm max}$ when it achieves its maximum (or
minimum). All three observables have the same cumulative probability
distribution expressed as an arcsine function, thus the name of arcsine laws.
We show how these laws change for fractional Brownian motion $X_t$, a
non-Markovian Gaussian process indexed by the Hurst exponent $H$. It
generalizes standard Brownian motion (i.e. $H=\tfrac{1}{2}$). We obtain the
three probabilities using a perturbative expansion in $\epsilon =
H-\tfrac{1}{2}$. While all three probabilities are different, this distinction
can only be made at second order in $\epsilon$. Our results are confirmed to
high precision by extensive numerical simulations.
