Quadratic variation of càdlàg semimartingales as a.s. limit of the normalized truncated variations

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.

References in corpus (2)

• The Play Operator, the Truncated Variation and the Generalisation of the Jordan Decomposition
• Riemann-Stieltjes integrals driven by irregular signals in Banach spaces and rate-independent characteristics of their irregularity

Cited by in corpus (1)

• On the quadratic variation of the model-free price paths with jumps