Feynman-Kac's representation in time-space domains and sensitivity with respect to the domain

Cristina Costantini; Nicole El Karoui; Emmanuel Gobet

doi:10.1016/S1631-073X(03)00364-9

Feynman-Kac's representation in time-space domains and sensitivity with respect to the domain

Titre traduit de la contribution: Représentation de Feynman-Kac dans des domaines temps-espace et sensibilité par rapport au domaine

Cristina Costantini
, Nicole El Karoui
, Emmanuel Gobet

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

We consider the solution X = (X_t)_t≥0 of a time-inhomogeneous stochastic differential equation and the exit time τ by (t, X_t)_t≥0 of the time-space domain D. We prove the differentiability of expectations of functionals of X stopped at τ, with respect to the domain D: these results extend those in the literature, known in particular by the analysts for the issues of shape optimization. However from the probabilistic point of view, this is not standard.

Titre traduit de la contribution	Représentation de Feynman-Kac dans des domaines temps-espace et sensibilité par rapport au domaine
langue originale	Anglais
Pages (de - à)	337-342
Nombre de pages	6
journal	Comptes Rendus Mathematique
Volume	337
Numéro de publication	5
Les DOIs	https://doi.org/10.1016/S1631-073X(03)00364-9
état	Publié - 1 sept. 2003

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10.1016/S1631-073X(03)00364-9

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abstract = "We consider the solution X = (Xt)t≥0 of a time-inhomogeneous stochastic differential equation and the exit time τ by (t, Xt)t≥0 of the time-space domain D. We prove the differentiability of expectations of functionals of X stopped at τ, with respect to the domain D: these results extend those in the literature, known in particular by the analysts for the issues of shape optimization. However from the probabilistic point of view, this is not standard.",

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Feynman-Kac's representation in time-space domains and sensitivity with respect to the domain

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