Gâteaux type path-dependent PDEs and BSDEs with Gaussian forward processes

Adrien Barrasso (1, 2) , Francesco Russo (3, 4)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées
2 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
3 UMA - Unité de Mathématiques Appliquées
4 OC - Optimisation et commande

We are interested in path-dependent semilinear PDEs, where the derivatives are of Gâteaux type in specific directions k and b, being the kernel functions of a Volterra Gaussian process X. Under some conditions on k, b and the coefficients of the PDE, we prove existence and uniqueness of a decoupled mild solution, a notion introduced in a previous paper by the authors. We also show that the solution of the PDE can be represented through BSDEs where the forward (underlying) process is X.

Mots clés: Gaussian processes; Volterra processes; path-dependent PDEs; decoupled mild solutions; BSDEs

Domaines: Probabilités [math.PR]

Adrien Barrasso, Francesco Russo. Gâteaux type path-dependent PDEs and BSDEs with Gaussian forward processes. Stochastics and Dynamics, 2022, 22, pp.2250007,. ⟨10.1142/S0219493722500071⟩. ⟨hal-02197479⟩