Derivatives Along a Curve and the Functional Stochastic Calculus

Christian Houdré; Jorge Víquez

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arXiv · 2604.10705

Derivatives Along a Curve and the Functional Stochastic Calculus

Christian Houdré·Jorge Víquez

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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.

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Christian Houdré, Jorge Víquez. 2026-04-12. Derivatives Along a Curve and the Functional Stochastic Calculus. https://arxiv.org/abs/2604.10705

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