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Isolated Zeros for Brownian Motion with Variable Drift


 
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1. Title Title of document Isolated Zeros for Brownian Motion with Variable Drift
 
2. Creator Author's name, affiliation, country Tonci Antunovic; University of California Berkeley; United States
 
2. Creator Author's name, affiliation, country Krzysztof Burdzy; University of Washington; United States
 
2. Creator Author's name, affiliation, country Yuval Peres; Microsoft Research; United States
 
2. Creator Author's name, affiliation, country Julia Ruscher; Technische Universität Berlin; Germany
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Brownian motion; Hölder continuity; Cantor function; isolated zeros; Hausdorff dimension
 
3. Subject Subject classification 60J65; 26A16; 26A30; 28A78
 
4. Description 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.
 
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7. Date (YYYY-MM-DD) 2011-09-27
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/927
 
10. Identifier Digital Object Identifier 10.1214/EJP.v16-927
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 16
 
12. Language English=en
 
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