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On pathwise quadratic variation for càdlàg functions

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. The definition then simplifies and one obtains the Lebesgue decomposition of the pathwise quadratic variation as a result, rather than requiring it as an extra condition.
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https://hal.archives-ouvertes.fr/hal-01818930
Contributor : Rama Cont <>
Submitted on : Wednesday, November 7, 2018 - 10:26:34 AM
Last modification on : Friday, April 10, 2020 - 5:27:05 PM
Document(s) archivé(s) le : Friday, February 8, 2019 - 1:40:03 PM

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  • HAL Id : hal-01818930, version 3

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Henry Chiu, Rama Cont. On pathwise quadratic variation for càdlàg functions. 2018. ⟨hal-01818930v3⟩

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