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 rough paths and fixed-point techniques, we study properties of the solutions. We also prove a convergence theorem and apply our results to differential equations driven by Brownian motions and fractional Brownian motions.

Mots clés: Ordinary differential equations; Rough path theory; Affine boundary value problem

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

Antoine Lejay, Renaud Marty. Rough differential equations with affine boundary conditions. 2023. ⟨hal-03626402v3⟩