Estimates for the Small Ball Probabilities of the Fractional Brownian Sheet
- Cite this article as:
- Dunker, T. Journal of Theoretical Probability (2000) 13: 357. doi:10.1023/A:1007897525164
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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 L2-Hölder-type condition.