Thomas Dunker

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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 can be estimated from below by exp(&C= &2 |log =| 2d&1), which(More)
Let X (t) := t 0 (s)W (s) ds; t¿0, where W (t); t¿0, is a standard Brownian motion and is a weight function. We determine the rate of −log P(sup t∈[0; 1] |X (t)| ¡ ¡); as → 0, for a large class of weight functions. The methods of our proofs are general and can be applied to many other problems. As an application, a Chung-type law of the iterated logarithm(More)
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