Characteristics and It{\^o}'s formula for weak Dirichlet processes: an equivalence result
Probability
2024-07-25 v1
Abstract
The main objective consists in generalizing a well-known It{\^o} formula of J. Jacod and A. Shiryaev: given a c{\`a}dl{\`a}g process S, there is an equivalence between the fact that S is a semimartingale with given characteristics (B^k , C, ) and a It{\^o} 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.
Cite
@article{arxiv.2407.17071,
title = {Characteristics and It{\^o}'s formula for weak Dirichlet processes: an equivalence result},
author = {Elena Bandini and Francesco Russo},
journal= {arXiv preprint arXiv:2407.17071},
year = {2024}
}