A law of the iterated logarithm for general lacunary series
Charles N. Moore ; Xiaojing Zhang
Colloquium Mathematicae, Tome 126 (2012), p. 95-103 / Harvested from The Polish Digital Mathematics Library
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We prove a law of the iterated logarithm for sums of the form ∑k=1Nakf(nkx) where the nk 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.

Publié le : 2012-01-01
EUDML-ID : urn:eudml:doc:286565 
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     title = {A law of the iterated logarithm for general lacunary series},
     journal = {Colloquium Mathematicae},
     volume = {126},
     year = {2012},
     pages = {95-103},
     zbl = {1241.42007},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm126-1-6}
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Charles N. Moore; Xiaojing Zhang. A law of the iterated logarithm for general lacunary series. Colloquium Mathematicae, Tome 126 (2012) pp. 95-103. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm126-1-6/