Quadratic variation along refining partitions: Constructions and examples
<p>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...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
| Published: |
Elsevier
2022
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| Summary: | <p>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 <em>coarsening</em>. This class is shown to include typical sample paths of Brownian motion, but also paths which are 1/2 -Hölder continuous. Finally, we show how to extend these constructions to higher dimensions.</p> |
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