Weak Dirichlet processes and generalized martingale problems

april, 2024
Publication type:
Paper in peer-reviewed journals
Stochastic Processs and Their Applications, vol. 170, pp. 104261
assets/images/icons/icon_arxiv.png 2205.03099
Keywords :
Weak Dirichlet processes; càdlàg semimartingales; jump processes; martingale problem; singular drift; random measure.
In this paper we explain how the notion of {\it 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 {\it 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.
    author={Elena Bandini and Francesco Russo },
    title={Weak Dirichlet processes and generalized martingale problems },
    doi={10.1016/j.spa.2023.104261 },
    journal={Stochastic Processs and Their Applications },
    year={2024 },
    volume={170 },