Derivatives Along a Curve and the Functional Stochastic Calculus
Probability
2026-04-14 v1
Abstract
Motivated by extending the functional stochastic calculus, to important functionals to which it does not apply, a notion of functional derivative along a curve is introduced. This new setting is developed by incorporating path-dependent directional extensions. Our results then focus on a comprehensive exploration of these derivatives and the insights they provide on the structure of functionals.
Cite
@article{arxiv.2604.10705,
title = {Derivatives Along a Curve and the Functional Stochastic Calculus},
author = {Christian Houdré and Jorge Víquez},
journal= {arXiv preprint arXiv:2604.10705},
year = {2026}
}