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

¹ Department of Physics, Technical University of Munich - James-Franck Straße, 85747 Garching, Germany, EU
² Akhiezer Institute for Theoretical Physics NSC KIPT - Akademicheskaya Str.1, 61108 Kharkov, Ukraine
³ School of Chemistry, Tel Aviv University - Ramat Aviv, Tel Aviv 69978, Israel
⁴ Department of Physics, Tampere University of Technology - FI-33101 Tampere, Finland, EU

^a metz@ph.tum.de

Received: 17 February 2011
Accepted: 21 March 2011

Abstract

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 ℘_Θ(t)≃t^{−1+π(2H−2)/(2Θ)} in terms of the Hurst exponent H and the wedge angle Θ. We discuss this scaling behaviour in connection with the reaction kinetics of FBM particles in a one-dimensional domain.