Derivatives Along a Curve and the Functional Stochastic Calculus
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
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| _version_ | 1866914467144531968 |
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| author | Houdré, Christian Víquez, Jorge |
| author_facet | Houdré, Christian Víquez, Jorge |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_10705 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Derivatives Along a Curve and the Functional Stochastic Calculus Houdré, Christian Víquez, Jorge Probability 60G51, 60H05, 60H30 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. |
| title | Derivatives Along a Curve and the Functional Stochastic Calculus |
| topic | Probability 60G51, 60H05, 60H30 |
| url | https://arxiv.org/abs/2604.10705 |