Journal of Theoretical Probability

, Volume 13, Issue 2, pp 357–382 | Cite as

Estimates for the Small Ball Probabilities of the Fractional Brownian Sheet

  • Thomas Dunker

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 L2-Hölder-type condition.

Gaussian field small ball probabilities 

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Copyright information

© Plenum Publishing Corporation 2000

Authors and Affiliations

  • Thomas Dunker
    • 1
  1. 1.Institut für StochastikFriedrich Schiller UniversitätJenaGermany

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