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A new proof of an old result by Pickands


 
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1. Title Title of document A new proof of an old result by Pickands
 
2. Creator Author's name, affiliation, country J.M.P. Albin; Chalmers University of Technology, Sweden
 
2. Creator Author's name, affiliation, country Hyemi Choi; Chonbuk National University, Korea
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Stationary Gaussian process; Pickands constant; extremes
 
3. Subject Subject classification 60G70; 60G15
 
4. Description Abstract Let $\{\xi(t)\}_{t\in[0,h]}$ be a stationary Gaussian process with covariance function $r$ such that $r(t) =1-C|t|^{\alpha}+o(|t|^{\alpha})$ as $t\to0$. We give a new and direct proof of a result originally obtained by Pickands, on the asymptotic behaviour as $u\to\infty$ of the probability $\Pr\{\sup_{t\in[0,h]}\xi(t)>u\}$ that the process $\xi$ exceeds the level $u$. As a by-product, we obtain a new expression for Pickands constant $H_\alpha$.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) National Research Foundation of Korea
 
7. Date (YYYY-MM-DD) 2010-09-12
 
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/1566
 
10. Identifier Digital Object Identifier 10.1214/ECP.v15-1566
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 15
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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