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Small ball probabilities for Gaussian random fields and tensor products of compact operators

✍ Scribed by Karol', Andrei; Nazarov, Alexander; Nikitin, Yakov


Book ID
124096379
Publisher
American Mathematical Society
Year
2008
Tongue
English
Weight
341 KB
Volume
360
Category
Article
ISSN
0002-9947

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Metric Entropy of Integration Operators
✍ T Dunker; W Linde; T Kühn; M.A Lifshits 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 146 KB

Let T d : L 2 ([0, 1] d ) Ä C([0, 1] d ) be the d-dimensional integration operator. We show that its Kolmogorov and entropy numbers decrease with order at least k &1 (log k) d&1Â2 . From this we derive that the small ball probabilities of the Brownian sheet on [0, 1] d under the C([0, 1] d )-norm ca