A law of the iterated logarithm for general lacunary series

@article{CharlesN2012,
abstract = {We prove a law of the iterated logarithm for sums of the form $∑_\{k=1\}^\{N\} a_\{k\}f(n_\{k\}x)$ where the $n_\{k\}$ satisfy a Hadamard gap condition. Here we assume that f is a Dini continuous function on ℝⁿ which has the property that for every cube Q of sidelength 1 with corners in the lattice ℤⁿ, f vanishes on ∂Q and has mean value zero on Q.},
author = {Charles N. Moore, Xiaojing Zhang},
journal = {Colloquium Mathematicae},
keywords = {law of the iterated logarithm; martingale},
language = {eng},
number = {1},
pages = {95-103},
title = {A law of the iterated logarithm for general lacunary series},
url = {http://eudml.org/doc/286565},
volume = {126},
year = {2012},
}

TY - JOUR
AU - Charles N. Moore
AU - Xiaojing Zhang
TI - A law of the iterated logarithm for general lacunary series
JO - Colloquium Mathematicae
PY - 2012
VL - 126
IS - 1
SP - 95
EP - 103
AB - We prove a law of the iterated logarithm for sums of the form $∑_{k=1}^{N} a_{k}f(n_{k}x)$ where the $n_{k}$ satisfy a Hadamard gap condition. Here we assume that f is a Dini continuous function on ℝⁿ which has the property that for every cube Q of sidelength 1 with corners in the lattice ℤⁿ, f vanishes on ∂Q and has mean value zero on Q.
LA - eng
KW - law of the iterated logarithm; martingale
UR - http://eudml.org/doc/286565
ER -