ABSTRACT
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.
Acknowledgments
The author would like to thank the anonymous referees for their valuable comments which led to improvement of this work.
Disclosure statement
No potential conflict of interest was reported by the authors.