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A lower bound in the law of the iterated logarithm for general lacunary series

100%

Moore C., Zhang X.

Studia Mathematica

2014

tom 222

nr 3

207-228

We prove a lower bound in a law of the iterated logarithm for sums of the form $∑_{k=1}^{N} a_{k}f(n_{k}x+c_{k})$ where f satisfies certain conditions and the $n_{k}$ satisfy the Hadamard gap condition $n_{k+1}/n_{k} ≥ q > 1$.

A law of the iterated logarithm for general lacunary series

100%

Moore C., Zhang X.

Colloquium Mathematicum

2012

tom 126

nr 1

95-103

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.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Studia Mathematica

2 Moore C.

2 Zhang X.

1 2014

1 2012

Wyniki wyszukiwania

A lower bound in the law of the iterated logarithm for general lacunary series

A law of the iterated logarithm for general lacunary series