# Pathwise integration with respect to paths of finite quadratic variation

Ananova, A
Cont, R

29 October 2016

## Journal:

Journal de Mathématiques Pures et Appliquées

## Last Updated:

2021-06-20T16:53:31.397+01:00

6

107

## DOI:

10.1016/j.matpur.2016.10.004

737-757

## abstract:

We study a pathwise integral with respect to paths of finite quadratic variation, defined as the limit of non-anticipative Riemann sums for gradient-type integrands. We show that the integral satisfies a pathwise isometry property, analogous to the well-known Ito isometry for stochastic integrals. This property is then used to represent the integral as a continuous map on an appropriately defined vector space of integrands. Finally, we obtain a pathwise ‘signal plus noise’ decomposition for regular functionals of an irregular path with non-vanishing quadratic variation, as a unique sum of a pathwise integral and a component with zero quadratic variation.

866699

Submitted

Journal Article