Asymptotic behavior of small ball probabilities (Q2769693)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Asymptotic behavior of small ball probabilities |
scientific article; zbMATH DE number 1701873
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Asymptotic behavior of small ball probabilities |
scientific article; zbMATH DE number 1701873 |
Statements
25 September 2002
0 references
small ball probabilities
0 references
Banach space valued random elements
0 references
Gaussian vectors
0 references
random fields
0 references
0.8946682
0 references
0 references
0.8850007
0 references
Asymptotic behavior of small ball probabilities (English)
0 references
This article is a survey of recent research about asymptotic behavior of small ball probabilities. The typical problem of the small ball probabilities is to investigate the asymptotic behavior of \(P{ ||X||<r},\) as \(r\) goes to zero, for a random vector \(X\) taking values in a normed space. The subject is known for long time to be hard but there was substantial progress during the last years. The author surveys the recent results with special focus on the fruitful connection between Gaussian small ball probabilities and analytical problems of approximation theory. The author presents several interesting open problems, too.NEWLINENEWLINEFor the entire collection see [Zbl 0968.00043].
0 references
