Path-dependent SDEs with jumps and irregular drift: well-posedness and Dirichlet properties
Probability
2022-11-08 v1
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.
Cite
@article{arxiv.2211.03444,
title = {Path-dependent SDEs with jumps and irregular drift: well-posedness and Dirichlet properties},
author = {Elena Bandini and Francesco Russo},
journal= {arXiv preprint arXiv:2211.03444},
year = {2022}
}