Abstract In this paper, with aid of large deviation formulas established in strong topology generated by Holder norm for $k$-dimensional Brownian motion, the paper obtained the functional sample path properties for subsequence's $C$-$R$} increments of $k$-dimensional Brownian motion in Holder norm, by which one can get the functional laws of iterated logarithm for $k$-dimensional Brownian motion.
WEI Qi-cai. Functional sample path properties for subsequence's $\boldsymbol{C}$-$\boldsymbol{R}$ increments of $k$-dimensional Brownian motion in Holder norm. Applied Mathematics A Journal of Chinese Universities, 2015, 30(3): 355-366.