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

Abstract

We study the survival probability and the corresponding first passage time density of fractional Brownian motion 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 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.

6 pages, 4 figures

References in corpus (9)

• In vivo anomalous diffusion and weak ergodicity breaking of lipid granules
• First-passage times in complex scale-invariant media
• Single particle tracking in systems showing anomalous diffusion: the role of weak ergodicity breaking
• Geometry-controlled kinetics
• Probing microscopic origins of confined subdiffusion by first-passage observables
• Single-File diffusion in a Box
• Generalized Elastic Model yields Fractional Langevin Equation
• Stochastic calculus for fractional Brownian motion with Hurst exponent $H>1/4$: A rough path method by analytic extension
• Kinetics of First Passage in a Cone

Cited by in corpus (21)

• Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion
• First passages in bounded domains: When is the mean first passage time meaningful?
• Spectral content of a single non-Brownian trajectory
• First-passage and first-hitting times of Levy flights and Levy walks
• Codifference as a practical tool to measure interdependence
• First Exit Times of Harmonically Trapped Particles: A Didactic Review
• Aging Scaled Brownian Motion
• Fractional Brownian motion in a finite interval: correlations effect depletion or accretion zones of particles near boundaries
• Reflected fractional Brownian motion in one and higher dimensions
• First passage statistics for aging diffusion in annealed and quenched disorder
• First Passage Times for a Tracer Particle in Single File Diffusion and Fractional Brownian Motion
• Probability density of the fractional Langevin equation with reflecting walls
• Survival probability of a Brownian motion in a planar wedge of arbitrary angle
• Anomalous Diffusion: Fractional Brownian Motion vs. Fractional Ito Motion
• Search efficiency of discrete fractional Brownian motion in a random distribution of targets
• Absence of confinement and non-Boltzmann stationary states of fractional Brownian motion in shallow external potentials
• Probability density of fractional Brownian motion and the fractional Langevin equation with absorbing walls
• First-passage dynamics of obstructed tracer particle diffusion in one-dimensional systems
• Observation time dependent mean first passage time of diffusion and sub-diffusion processes
• Tempered fractional Brownian motion on finite intervals
• Vicious accelerating walkers