Metric Entropy and the Small Ball Problem for Gaussian Measures

Metric Entropy of Integration Operators

Metric Entropy of Integration Operators and Small Ball Probabilities for the Brownian Sheet

✍ 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