Abstract
We revisit Föllmer’s concept of quadratic variation of a càdlàg function along a sequence of time partitions and discuss its relation with the Skorokhod topology. We show that in order to obtain a robust notion of pathwise quadratic variation applicable to sample paths of càdlàg processes, one must reformulate the definition of pathwise quadratic variation as a limit in Skorokhod topology of discrete approximations along the partition. One then obtains a simpler definition which implies the Lebesgue decomposition of the pathwise quadratic variation as a result, rather than requiring it as an extra condition.
Citation
Henry Chiu. Rama Cont. "On pathwise quadratic variation for càdlàg functions." Electron. Commun. Probab. 23 1 - 12, 2018. https://doi.org/10.1214/18-ECP186
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