Path dependent equations driven by Hölder processes

Rafael Andretto Castrequini (1) , Francesco Russo (1, 2)

1 UMA - Unité de Mathématiques Appliquées
2 OC - Optimisation et commande

This paper investigates existence results for path-dependent differential equations driven by a Hölder function where the integrals are understood in the Young sense. The two main results are proved via an application of Schauder theorem and the vector field is allowed to be unbounded. The Hölder function is typically the trajectory of a stochastic process.

Mots clés: Young integration; Path-dependent; Differential equations

Domaines: Probabilités [math.PR]

Rafael Andretto Castrequini, Francesco Russo. Path dependent equations driven by Hölder processes. Stochastic Analysis and Applications, 2019, 37 (3), pp.480-498. ⟨10.1080/07362994.2019.1585263⟩. ⟨hal-01388433⟩