@article{EJP927,
author = {Tonci Antunovic and Krzysztof Burdzy and Yuval Peres and Julia Ruscher},
title = {Isolated Zeros for Brownian Motion with Variable Drift},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {16},
year = {2011},
keywords = {Brownian motion; Hölder continuity; Cantor function; isolated zeros; Hausdorff dimension},
abstract = {It is well known that standard one-dimensional Brownian motion $B(t)$ has no isolated zeros almost surely. We show that for any $\alpha<1/2$ there are alpha-Hölder continuous functions $f$ for which the process $B-f$ has isolated zeros with positive probability. We also prove that for any continuous function $f$, the zero set of $B-f$ has Hausdorff dimension at least $1/2$ with positive probability, and $1/2$ is an upper bound on the Hausdorff dimension if $f$ is $1/2$-Hölder continuous or of bounded variation.},
pages = {no. 65, 1793-1814},
issn = {1083-6489},
doi = {10.1214/EJP.v16-927},
url = {http://ejp.ejpecp.org/article/view/927}}