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Derivatives Along a Curve and the Functional Stochastic Calculus
Christian Houdré, Jorge Víquez · 2026-04-12 · via math.PR updates on arXiv.org

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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