Pathwise integration with respect to paths of finite quadratic variation

Author: 

Ananova, A
Cont, R

Publication Date: 

29 October 2016

Journal: 

Journal de Mathématiques Pures et Appliquées

Last Updated: 

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

Issue: 

6

Volume: 

107

DOI: 

10.1016/j.matpur.2016.10.004

page: 

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.

Symplectic id: 

866699

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article