We study the first-passage time, the distribution of the maximum, and the absorption probability of fractional Brownian motion of Hurst parameter $H$ with both a linear and a nonlinear drift. The latter appears naturally when applying nonlinear variable transformations. Via a perturbative expansion in $\varepsilon =H-1/2$, we give the first-order corrections to the classical result for Brownian motion analytically. Using a recently introduced adaptive-bisection algorithm, which is much more efficient than the standard Davies-Harte algorithm, we test our predictions for the first-passage time on grids of effective sizes up to $N_{\mathrm{eff}}=2^{28}\approx 2.7\times {10}^8$ points. The agreement between theory and simulations is excellent, and by far exceeds in precision what can be obtained by scaling alone.

• Received 13 October 2019
• Revised 21 February 2020
• Accepted 30 June 2020

DOI:https://doi.org/10.1103/PhysRevE.102.022102