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arXiv · 1004.2994

Strassen's invariance principle for random walk in random environment

Guangyu Yang·Yu Miao·Dihe Hu
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Abstract

In this paper, we consider random walk in random environment on $\mathbb{Z}^{d}\,(d\geq1)$ and prove the Strassen's strong invariance principle for this model, via martingale argument and the theory of fractional coboundaries of Derriennic and Lin \cite{DL}, under some conditions which require the variance of the quenched mean has a subdiffusive bound. The results partially fill the gaps between law of large numbers and central limit theorems.

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Guangyu Yang, Yu Miao, Dihe Hu. 2010-04-18. Strassen's invariance principle for random walk in random environment. https://arxiv.org/abs/1004.2994

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