Strassen's invariance principle for random walk in random environment [article]

Guangyu Yang, Yu Miao, Dihe Hu
2010 arXiv   pre-print
In this paper, we consider random walk in random environment on Z^d (d≥1) and prove the Strassen's strong invariance principle for this model, via martingale argument and the theory of fractional coboundaries of Derriennic and Lin 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.
arXiv:1004.2994v1 fatcat:n4ymy3nhg5egxlpbhufdl3infq