2018/01/01 by Henry Chiu, Rama Cont · 13 citations
Mathematics · #Applied mathematics #Brownian motion #Combinatorics #Geometry #Mathematical Approximation and Integration #Mathematical analysis #Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #Quadratic equation #Quadratic variation #Statistics #Variation (astronomy) #math.CA #math.PR
paper · pdf · open access · doi:10.1214/18-ecp186
published in Electronic Communications in Probability 23(none) (Institute of Mathematical Statistics) · arXiv admin note: text overlap with arXiv:1704.00654
openalex publication_date 2018/01/01 · arxiv created 2018/10/30 · arxiv updated 2019/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.