On small deviations of Gaussian processes using majorizing measures

Michel J. G. Weber. "On small deviations of Gaussian processes using majorizing measures." Colloquium Mathematicae 129.1 (2012): 41-59. <http://eudml.org/doc/284360>.

@article{MichelJ2012,
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.},
author = {Michel J. G. Weber},
journal = {Colloquium Mathematicae},
keywords = {small deviations; Gaussian processes; entropy numbers; majorizing measure method; ultrametric Gaussian processes},
language = {eng},
number = {1},
pages = {41-59},
title = {On small deviations of Gaussian processes using majorizing measures},
url = {http://eudml.org/doc/284360},
volume = {129},
year = {2012},
}

TY - JOUR
AU - Michel J. G. Weber
TI - On small deviations of Gaussian processes using majorizing measures
JO - Colloquium Mathematicae
PY - 2012
VL - 129
IS - 1
SP - 41
EP - 59
AB - 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.
LA - eng
KW - small deviations; Gaussian processes; entropy numbers; majorizing measure method; ultrametric Gaussian processes
UR - http://eudml.org/doc/284360
ER -