Estimates of entropy numbers in probabilistic setting

Estimates of entropy numbers in probabilistic setting

In this paper, we define the entropy number in probabilistic setting and determine the exact order of entropy number of finite-dimensional space in probabilistic setting. Moreover, we also estimate the sharp order of entropy number of univariate Sobolev space in probabilistic setting by discretizati...

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Veröffentlicht in:Open mathematics (Warsaw, Poland) Poland), 2020-12, Vol.18 (1), p.1635-1644
Hauptverfasser: Han, Yongjie, Xiao, Hanyue, Chen, Guanggui
Format: Artikel
Sprache:eng
Schlagworte:
41A46
42A61
46C99
entropy numbers
finite-dimensional
Gaussian measure
probabilistic setting
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Zusammenfassung:In this paper, we define the entropy number in probabilistic setting and determine the exact order of entropy number of finite-dimensional space in probabilistic setting. Moreover, we also estimate the sharp order of entropy number of univariate Sobolev space in probabilistic setting by discretization method.
ISSN:2391-5455
2391-5455
DOI:10.1515/math-2020-0121