Electronic Communications in Probability

On pathwise quadratic variation for càdlàg functions

Henry Chiu and Rama Cont

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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.

Article information

Source
Electron. Commun. Probab., Volume 23 (2018), paper no. 85, 12 pp.

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1542942174

Digital Object Identifier
doi:10.1214/18-ECP186

Mathematical Reviews number (MathSciNet)
MR3882226

Zentralblatt MATH identifier
07023471

Subjects
Primary: 60H05: Stochastic integrals 26B35: Special properties of functions of several variables, Hölder conditions, etc.

Keywords
quadratic variation semimartingale pathwise calculus Ito formula pathwise integration cadlag functions Skorokhod topology

Rights
Creative Commons Attribution 4.0 International License.

Citation

Chiu, Henry; Cont, Rama. On pathwise quadratic variation for càdlàg functions. Electron. Commun. Probab. 23 (2018), paper no. 85, 12 pp. doi:10.1214/18-ECP186. https://projecteuclid.org/euclid.ecp/1542942174


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References

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