The first exit time of fractional Brownian motion from a parabolic domain

TL;DR

This paper investigates the distribution of the first exit time for multi-dimensional fractional Brownian motion from parabola-shaped unbounded domains, focusing on the behavior of the upper tail of this distribution.

Contribution

It provides new insights into the tail behavior of the first exit time for fractional Brownian motion in complex unbounded domains, a topic not extensively explored before.

Findings

Characterization of the upper tail of the exit time distribution

Extension of exit time analysis to multi-dimensional fractional Brownian motion

Insights into the influence of domain shape on exit time behavior

Abstract

We study the first exit time of a multi-dimensional fractional Brownian motion from unbounded domains. In particular, we are interested in the upper tail of the corresponding distribution when the domain is parabola-shaped.