Invariant imbedding and rough differential equations with affine boundary conditions

Antoine Lejay (1, 2) , Renaud Marty (2)

1 PASTA - Processus aléatoires spatio-temporels et leurs applications
2 IECL - Institut Élie Cartan de Lorraine

In this paper we consider rough differential equations with affine boundary conditions. Using invariant imbedding techniques, we study qualitative properties of the solutions. We also prove a Wonk-Zakai theorem to apply our results to differential equations driven by Brownian motions and fractional Brownian motions.

Mots clés: Ordinary differential equations; Rough paths theory; Invariant imbedding; Two-point affine boundary value problem

Domaines: Analyse classique [math.CA]; Probabilités [math.PR]

Antoine Lejay, Renaud Marty. Invariant imbedding and rough differential equations with affine boundary conditions. 2023. ⟨hal-03626402v2⟩