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.

中文翻译：

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限制在与伯努利随机场的迭代对数定律相关的最大函数上

我们为严格平稳随机场的迭代对数有界定律提供了充分条件，当求和在矩形上进行时，该随机场可表示为 iid 随机场的函数。该研究是通过控制适当的最大函数的矩来完成的。给出了线性随机场泛函、高斯线性随机场函数和沃尔泰拉过程的应用。