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Small ball probabilities for integrals of weighted Brownian motion

✍ Scribed by T. Dunker; W.V. Li; W. Linde

Book ID
104303184
Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
87 KB
Volume
46
Category
Article
ISSN
0167-7152

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πŸ“œ SIMILAR VOLUMES

Metric Entropy of Integration Operators
Metric Entropy of Integration Operators and Small Ball Probabilities for the Brownian Sheet
✍ T Dunker; W Linde; T KΓΌhn; M.A Lifshits πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 146 KB

Let T d : L 2 ([0, 1] d ) Γ„ 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&1Γ‚2 . 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