ON SOJOURN OF BROWNIAN MOTION INSIDE MOVING BOUNDARIES

Stéphane Seuret (1) , Xiaochuan Yang (1)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

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

Mots clés: macroscopic Hausdorff dimension; sojourn times; Brownian motion

Domaines: Probabilités [math.PR]

Stéphane Seuret, Xiaochuan Yang. ON SOJOURN OF BROWNIAN MOTION INSIDE MOVING BOUNDARIES. Stochastic Processes and their Applications, 2019, 129 (3), pp.978-994. ⟨10.1016/j.spa.2018.04.002⟩. ⟨hal-01612294⟩