  We present several constructions of paths and processes with finite quadratic
variation along a refining sequence of partitions, extending previous
constructions to the non-uniform case. We study in particular the dependence of
quadratic variation with respect to the sequence of partitions for these
constructions. We identify a class of paths whose quadratic variation along a
partition sequence is invariant under {\it coarsening}. This class is shown to
include typical sample paths of Brownian motion, but also paths which are
$\frac{1}{2}$-H\"older continuous. Finally, we show how to extend these
constructions to higher dimensions.

Probability;Classical Analysis and ODEs