On small deviations of Gaussian processes using majorizing measures

• Autorzy: Michel J. G. Weber
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 60G50: Sums of independent random variables; random walks
• 60F15: Strong theorems
• 60F05: Central limit and other weak theorems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2012
• Tom: 129
• Numer: 1
• Strony: 41-59

Daty

wydano

2012

Twórcy

autor

Michel J. G. Weber

• Université Louis-Pasteur et C.N.R.S., 7 rue René Descartes, 67084 Strasbourg Cedex, France

Identyfikatory

DOI

10.4064/cm129-1-3