Sojourn time dimensions of fractional Brownian motion

TL;DR

This paper investigates the size and structure of the sets of times when fractional Brownian motion stays within a certain boundary, using large-scale dimensional analysis.

Contribution

It provides a detailed description of the size of sojourn time sets for fractional Brownian motion using large-scale dimensions, a novel analysis in this context.

Findings

Characterization of the size of sojourn time sets

Application of large-scale dimensions to fractional Brownian motion

Insights into the boundary behavior of fractional Brownian motion

Abstract

We describe the size of the sets of sojourn times $E_\gamma =\{t\geq 0: |B_t|\leq t^\gamma\}$ associated with a fractional Brownian motion $B$ in terms of various large scale dimensions.