Bound on the maximal function associated to the law of the iterated logarithms for Bernoulli random fields

Davide Giraudo

doi:10.1080/17442508.2021.1920942

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arXiv · 1909.10943

Bound on the maximal function associated to the law of the iterated logarithms for Bernoulli random fields

Davide Giraudo

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Abstract

We provide a sufficient condition for the bounded law of the iterated logarithms for strictly stationary random fields expressable as a functional of i.i.d. random fields when the summation is done on rectangles. The study is done via the control of the moments of an appropriated maximal function. Applications to functionals of linear random fields, functions of a Gaussian linear random field and Volterra process are given.

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BibTeX RIS

Davide Giraudo. 2019-09-24. Bound on the maximal function associated to the law of the iterated logarithms for Bernoulli random fields. https://doi.org/10.1080/17442508.2021.1920942

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