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2018 On pathwise quadratic variation for càdlàg functions
Henry Chiu, Rama Cont
Electron. Commun. Probab. 23: 1-12 (2018). DOI: 10.1214/18-ECP186

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

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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

Information

Received: 19 June 2018; Accepted: 30 October 2018; Published: 2018
First available in Project Euclid: 23 November 2018

zbMATH: 07023471
MathSciNet: MR3882226
Digital Object Identifier: 10.1214/18-ECP186

Subjects:
Primary: 26B35 , 60H05

Keywords: cadlag functions , Ito formula , pathwise calculus , pathwise integration , Quadratic Variation , Semimartingale , Skorokhod topology

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