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We present an algorithm to efficiently sample first-passage times forfractional Brownian motion. To increase the resolution, an initial coarselattice is successively refined close to the target, by adding exactly sampledmidpoints, where the probability that they reach the target is non-negligible.Compared to a path of $N$ equally spaced points, the algorithm achieves thesame numerical accuracy $N_{\rm eff}$, while sampling only a small fraction ofall points. Though this induces a statistical error, the latter is bounded foreach bridge, allowing us to bound the total error rate by a number of ourchoice, say $P_{\rm error}^{\rm tot}=10^{-6}$. This leads to significantimprovements in both memory and speed. For $H=0.33$ and $N_{\rm eff}=2^{32}$,we need $5\,000$ times less CPU time and $10\, 000$ times less memory than theclassical Davies Harte algorithm. The gain grows for $H=0.25$ and $N_{\rm eff}= 2^{42}$ to $3\cdot 10^{5}$ for CPU and $10^6$ for memory. We estimate ouralgorithmic complexity as ${\cal C}^{\rm ABSec}(N_{\rm eff}) = {\calO}\left(\left( \ln N_{\rm eff}\right)^{3}\right)$, to be compared to DaviesHarte which has complexity ${\cal C}^{\rm DH}(N) = {\cal O}\left(N \ln N\right)$. Decreasing $P_{\rm error}^{\rm tot}$ results in a small increase incomplexity, proportional to $\ln (1/P_{\rm error}^{\rm tot})$. Our currentimplementation is limited to the values of $N_{\rm eff}$ given above, due to aloss of floating-point precision. The algorithm can be adapted to other extremeevents and arbitrary Gaussian processes. It enables one to numerically validatetheoretical predictions that were hitherto inaccessible.

Sampling first-passage times of fractional Brownian Motion using adaptive bisections