Electronic Communications in Probability

On pathwise quadratic variation for càdlàg functions

Henry Chiu and Rama Cont

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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

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

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

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Zentralblatt MATH identifier

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

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

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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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