On pathwise quadratic variation for cadlag functions

Abstract

We revisit H. Foellmer's concept of quadratic variation of a cadlag 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 cadlag 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 of quadratic variation which implies the Lebesgue decomposition as a result, rather than requiring it as an extra condition.

arXiv commentarXiv admin note: text overlap with arXiv:1704.00654

References in corpus (4)

• Pathwise integration with respect to paths of finite quadratic variation
• Pathwise integration and change of variable formulas for continuous paths with arbitrary regularity
• Local times for typical price paths and pathwise Tanaka formulas
• Weak approximation of martingale representations

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