A law of the iterated logarithm for general lacunary series
Charles N. Moore; Xiaojing Zhang
Colloquium Mathematicae (2012)
- Volume: 126, Issue: 1, page 95-103
- ISSN: 0010-1354
Access Full Article
top
Abstract
topHow to cite
topCharles N. Moore, and Xiaojing Zhang. "A law of the iterated logarithm for general lacunary series." Colloquium Mathematicae 126.1 (2012): 95-103. <http://eudml.org/doc/286565>.
@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 -
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.