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

TL;DR

This paper investigates the first passage behavior of fractional Brownian motion within two-dimensional wedge domains, revealing a specific long-time scaling law for the first passage time density based on the Hurst exponent and wedge angle.

Contribution

It provides an analytical and numerical analysis of the first passage time density for FBM in wedge domains, highlighting a new scaling law related to H and Theta.

Findings

The first passage time density scales as t^{-1+pi*(2H-2)/(2*Theta)} in long time limit.

The scaling law connects FBM first passage behavior with reaction kinetics in one-dimensional domains.

Numerical simulations confirm the analytical predictions.

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.