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Article Dans Une Revue Electronic Communications in Probability Année : 2018

On pathwise quadratic variation for càdlàg functions

Résumé

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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Dates et versions

hal-01818930 , version 1 (19-06-2018)
hal-01818930 , version 2 (21-06-2018)
hal-01818930 , version 3 (07-11-2018)

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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. Electronic Communications in Probability, 2018, 23. ⟨hal-01818930v3⟩
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