Weak Dirichlet processes and generalized martingale problems
april, 2024
Publication type:
Paper in peer-reviewed journals
Journal:
Stochastic Processs and Their Applications, vol. 170, pp. 104261
Download:
HAL:
arXiv:
Keywords :
Weak Dirichlet processes; càdlàg semimartingales; jump processes;
martingale problem; singular drift; random measure.
Abstract:
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.
BibTeX:
@article{Ban-Rus-2024, 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 }, month={4}, volume={170 }, pages={104261}, }