On sojourn of Brownian motion inside moving boundaries

2017/06/14 by Stephane Seuret, Seuret, Stephane, Xiaochuan Yang +1
Mathematics · #FOS: Mathematics #Metric Geometry (math.MG) #Probability (math.PR) #math.MG #math.PR

paper · pdf · doi:10.48550/arxiv.1706.04519

16 pages. The proofs are simplified in the revision

arxiv created 2018/01/28 · arxiv updated 2018/01/30

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.

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