# On sojourn of Brownian motion inside moving boundaries

## TL;DR

This paper studies the large-scale structure of Brownian motion's sojourn sets within moving boundaries, calculating various dimensions and densities, and providing a uniform dimension result for level sets.

## Contribution

It introduces new calculations of macroscopic dimensions and densities for Brownian sojourn sets within moving boundaries, advancing understanding of their large-scale geometric properties.

## Key findings

- Computed macroscopic Hausdorff dimension of sojourn sets
- Determined upper mass dimension and logarithmic density
- Established a uniform macroscopic dimension result for level sets

## Abstract

We investigate the large scale structure of certain sojourn sets of one dimensional Brownian motion within two-sided moving boundaries. The macroscopic Hausdorff dimension, upper mass dimension and logarithmic density of these sets are computed. We also give a uniform macroscopic dimension result for the Brownian level sets.