Journal of Theoretical Probability

, Volume 13, Issue 2, pp 357–382

Estimates for the Small Ball Probabilities of the Fractional Brownian Sheet

  • Thomas Dunker
Article

DOI: 10.1023/A:1007897525164

Cite this article as:
Dunker, T. Journal of Theoretical Probability (2000) 13: 357. doi:10.1023/A:1007897525164

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 fieldsmall ball probabilities

Copyright information

© Plenum Publishing Corporation 2000

Authors and Affiliations

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