, Volume 13, Issue 2, pp 357-382

Estimates for the Small Ball Probabilities of the Fractional Brownian Sheet

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Abstract

We obtain some new estimates for the small ball behavior of the d-dimensional fractional Brownian sheet under Hölder and Orlicz norms. For d=2, these bounds are sharp for the Orlicz and the sup-norm. In addition, we give bounds for the Kolmogorov and entropy numbers of some operators satisfying an L 2-Hölder-type condition.