Path-dependent SDEs with jumps and irregular drift: well-posedness and Dirichlet properties

Elena Bandini and Francesco Russo

submitted

Publication type:

Paper in peer-reviewed journals

HAL:

hal-03840544

arXiv:

2211.03444

Keywords :

Path-dependent SDEs; Dirichlet processes; Random measure; Singular drift.

Abstract:

We discuss a concept of path-dependent SDE with distributional drift with possible jumps. We interpret it via a suitable martingale problem, for which we provide existence and uniqueness. The corresponding solutions are expected to be Dirichlet processes, nevertheless we give examples of solutions which do not fulfill this property. In the second part of the paper we indeed state and prove significant new results on the class of Dirichlet processes.

BibTeX:

@article{Ban-Rus-2200-1,
    author={Elena Bandini and Francesco Russo },
    title={Path-dependent SDEs with jumps and irregular drift: 
           well-posedness and Dirichlet properties },
    year={submitted },
    month={11},
}