Abstract
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.
Original language | Undefined/Unknown |
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Journal | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS |
Volume | 512 |
Issue number | 2 |
Publication status | Published - 26 Sept 2021 |
Keywords
- math.PR
- math.CA