Maximal function associated to the bounded law of the iterated logarithms via orthomartingale approximation

摘要

We give sufficient conditions for the bounded law of the iterated logarithms for strictly stationary random fields when the summation is done on rectangle. The study is done by the control of an appropriated maximal function. The case of orthomartingales is treated. Then results on projective conditions are derived. (C) 2020 Elsevier Inc. All rights reserved.