2017/08/02 by Rafał M. Łochowski, Łochowski, Rafał M.
Economics, Econometrics and Finance · Mathematics · #60G48 #60H05 #FOS: Mathematics #Mathematical Dynamics and Fractals #Nonlinear Differential Equations Analysis #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1708.00732
openalex publication_date 2017/08/02 · openalex created_date 2017/08/08 · openalex updated_date 2026/07/28
For a real càdlàg path x we define sequence of semi-explicit quantities, which do not depend on any partitions and such that whenever x is a path of a càdlàg semimartingale then these quantities tend a.s. to the continuous part of the quadratic variation of the semimartingale. Next, we derive several consequences of this result and propose a new approach to define Föllmer's pathwise integral.