A+ CATEGORY SCIENTIFIC UNIT

On small deviations of Gaussian processes using majorizing measures

Volume 129 / 2012

Michel J. G. Weber Colloquium Mathematicum 129 (2012), 41-59 MSC: Primary 60F15, 60G50; Secondary 60F05. DOI: 10.4064/cm129-1-3

Abstract

We give two examples of periodic Gaussian processes, having entropy numbers of exactly the same order but radically different small deviations. Our construction is based on Knopp's classical result yielding existence of continuous nowhere differentiable functions, and more precisely on Loud's functions. We also obtain a general lower bound for small deviations using the majorizing measure method. We show by examples that our bound is sharp. We also apply it to Gaussian independent sequences and to a generic class of ultrametric Gaussian processes.

Authors

  • Michel J. G. WeberUniversité Louis-Pasteur et C.N.R.S.
    7 rue René Descartes
    67084 Strasbourg Cedex, France
    e-mail

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image