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Random Gaussian Sums on Trees


 
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1. Title Title of document Random Gaussian Sums on Trees
 
2. Creator Author's name, affiliation, country Mikhail Lifshits; St. Petersburg State University; Russian Federation
 
2. Creator Author's name, affiliation, country Werner Linde; FSU Jena; Germany
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Gaussian processes, processes indexed by trees, bounded processes, summation on trees, metric entropy
 
3. Subject Subject classification 60G15; 06A06,; 05C05
 
4. Description Abstract Let $T$ be a tree with induced partial order. We investigate a centered Gaussian process $X$ indexed by $T$ and generated by weight functions. In a first part we treat general trees and weights and derive necessary and sufficient conditions for the a.s. boundedness of $X$ in terms of compactness properties of $(T,d)$. Here $d$ is a special metric defined by the weights, which, in general, is not comparable with the Dudley metric generated by $X$. In a second part we investigate the boundedness of $X$ for the binary tree. Assuming some mild regularity assumptions about on weight, we completely characterize homogeneous weights with $X$ being a.s. bounded.
 
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7. Date (YYYY-MM-DD) 2011-04-12
 
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/871
 
10. Identifier Digital Object Identifier 10.1214/EJP.v16-871
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 16
 
12. Language English=en
 
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