Quadratic variation along refining partitions: Constructions and Examples

Rama Cont; Purba Das

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arXiv · 2109.12635

Quadratic variation along refining partitions: Constructions and Examples

Rama Cont·Purba Das

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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.

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Rama Cont, Purba Das. 2021-09-26. Quadratic variation along refining partitions: Constructions and Examples. https://arxiv.org/abs/2109.12635

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