The influence of a log-type small ball factor in the study of the lower classes

  • El-Nouty C
  • 1

    Readers

    Mendeley users who have this article in their library.
  • 4

    Citations

    Citations of this article.

Abstract

Let {BH1,H2 (t1, t2), t1 ≥ 0, t2 ≥ 0} be a fractional Brownian sheet with indexes 0 < H1, H2 < 1. When H1 = H2 := H, there is a logarithmic factor in the small ball function of the sup-norm statistic of BH,H. First, we state general conditions (one based on a logarithmic factor in the small ball function) on some statistics of BH,H. Then we characterize the sufficiency part of the lower classes of these statistics by an integral test. Finally, when we consider the sup-norm statistic, the influence of the log-type small ball factor in the necessity part is measured by a second integral test. © 2004 Elsevier SAS. All rights reserved.

Author-supplied keywords

  • Fractional Brownian sheet
  • Lower classes
  • Small ball probabilities

Get free article suggestions today

Mendeley saves you time finding and organizing research

Sign up here
Already have an account ?Sign in

Find this document

Authors

  • Charles El-Nouty

Cite this document

Choose a citation style from the tabs below

Save time finding and organizing research with Mendeley

Sign up for free