On norms in some class of exponential type Orlicz spaces of random variables
A new characterization of the exponential type Orlicz spaces generated by the functions exp ( | x | p ) - 1 ( p ≥ 1 ) is given. We define norms for centered random variables belonging to these spaces. We show equivalence of these norms with the Luxemburg norms. On the example of Hoeffding’s inequali...
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| Veröffentlicht in: | Positivity : an international journal devoted to the theory and applications of positivity in analysis 2020-11, Vol.24 (5), p.1231-1240 |
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| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | A new characterization of the exponential type Orlicz spaces generated by the functions
exp
(
|
x
|
p
)
-
1
(
p
≥
1
) is given. We define norms for centered random variables belonging to these spaces. We show equivalence of these norms with the Luxemburg norms. On the example of Hoeffding’s inequality we present some application of these norms in a probabilistic context. |
|---|---|
| ISSN: | 1385-1292 1572-9281 |
| DOI: | 10.1007/s11117-019-00729-6 |