Pathwise integration with respect to paths of finite quadratic variation
Integration trajectorielle par rapport aux trajectoires à variation quadratique finie
Résumé
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.
Origine : Fichiers produits par l'(les) auteur(s)
Loading...