Characteristics and Itô's formula for weak Dirichlet processes: an equivalence result

Elena Bandini (1) , Francesco Russo (2, 3)

1 UNIBO - Alma Mater Studiorum Università di Bologna = University of Bologna
2 OC - Optimisation et commande
3 ENSTA Paris - École Nationale Supérieure de Techniques Avancées

The main objective consists in generalizing a well-known Itô formula of J. Jacod and A. Shiryaev: given a càdlàg process S, there is an equivalence between the fact that S is a semimartingale with given characteristics (B^k , C, ν) and a Itô formula type expansion of F (S), where F is a bounded function of class C2. This result connects weak solutions of path-dependent SDEs and related martingale problems. We extend this to the case when S is a weak Dirichlet process. A second aspect of the paper consists in discussing some untreated features of stochastic calculus for finite quadratic variation processes.

Mots clés: Martingale problem; Itô formula; weak Dirichlet process; Characteristics

Domaines: Mathématiques [math]

Elena Bandini, Francesco Russo. Characteristics and Itô's formula for weak Dirichlet processes: an equivalence result. 2023. ⟨hal-04019358⟩