Weak Dirichlet processes and generalized martingale problems
Probability
2022-07-04 v2
Abstract
In this paper we explain how the notion of ''weak Dirichlet process'' is the suitable generalization of the one of semimartingale with jumps. For such a process we provide a unique decomposition which is new also for semimartingales: in particular we introduce ''characteristics'' for weak Dirichlet processes. We also introduce a weak concept (in law) of finite quadratic variation. We investigate a set of new useful chain rules and we discuss a general framework of (possibly path-dependent with jumps) martingale problems with a set of examples of SDEs with jumps driven by a distributional drift.
Cite
@article{arxiv.2205.03099,
title = {Weak Dirichlet processes and generalized martingale problems},
author = {Elena Bandini and Francesco Russo},
journal= {arXiv preprint arXiv:2205.03099},
year = {2022}
}