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Invariance principles for standard-normalized and self-normalized random fields

Mohamed El Machkouri·Lahcen Ouchti
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Abstract

We investigate the invariance principle for set-indexed partial sums of a stationary field $(X\_{k})\_{k\in\mathbb{Z}^{d}}$ of martingale-difference or independent random variables under standard-normalization or self-normalization respectively.

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Mohamed El Machkouri, Lahcen Ouchti. 2005-02-07. Invariance principles for standard-normalized and self-normalized random fields. https://arxiv.org/abs/math/0502135

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