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

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.

References in corpus (3)

• Exponential inequalities for self-normalized martingales with applications
• On the normal approximation for random fields via martingale methods
• Convergence rates in the central limit theorem for weighted sums of Bernoulli random fields