Volume 94, Number 2, April 2011
|Number of page(s)||6|
|Published online||18 April 2011|
First passage behaviour of fractional Brownian motion in two-dimensional wedge domains
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
Accepted: 21 March 2011
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.
PACS: 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 02.50.Ey – Stochastic processes / 87.10.Mn – Stochastic modeling
© EPLA, 2011
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