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Uniform Upper Bound for a Stable Measure of a Small Ball


 
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1. Title Title of document Uniform Upper Bound for a Stable Measure of a Small Ball
 
2. Creator Author's name, affiliation, country Michal Ryznar; Wroclaw University of Technology
 
2. Creator Author's name, affiliation, country Tomasz Zak; Wroclaw University of Technology
 
3. Subject Discipline(s) Mathematics
 
3. Subject Keyword(s) stable measure, small ball
 
3. Subject Subject classification 60B11, 69E07
 
4. Description Abstract P. Hitczenko, S.Kwapien, W.N.Li, G.Schechtman, T.Schlumprecht and J.Zinn stated the following conjecture. Let $\mu$ be a symmetric $\alpha$-stable measure on a separable Banach space and $B$ a centered ball such that $\mu(B)\le b$. Then there exists a constant $R(b)$, depending only on $b$, such that $\mu(tB)\le R(b)t\mu(B)$ for all $0 < t < 1$. We prove that the above inequality holds but the constant $R$ must depend also on $\alpha$.
 
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6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 1998-09-16
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/995
 
10. Identifier Digital Object Identifier 10.1214/ECP.v3-995
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 3
 
12. Language English=en en
 
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