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

Elena Bandini and Francesco Russo

submitted

Publication type:

Paper in peer-reviewed journals

HAL:

hal-04019358

Keywords :

Martingale problem; Itô formula; weak Dirichlet process; Characteristics

Abstract:

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.

BibTeX:

@article{Ban-Rus-2200-2,
    author={Elena Bandini and Francesco Russo },
    title={Characteristics and Itô's formula for weak Dirichlet 
           processes: an equivalence result },
    year={submitted },
    month={3},
}