First passage behaviour of fractional Brownian motion in two-dimensional wedge domains

We study the survival probability and the corresponding first passage time density of fractional Brownian motion (FBM) confined to a two-dimensional open wedge domain with absorbing boundaries. By analytical arguments and numerical simulation we show that in the long-time limit the first passage time density scales as p(Theta)(t) similar or equal to t(-1+pi(2H-2)/(2 Theta)) in terms of the Hurst exponent H and the wedge angle Theta. We discuss this scaling behaviour in connection with the reaction kinetics of FBM particles in a one-dimensional domain. Copyright (C) EPLA, 2011