Weak Dirichlet processes and generalized martingale problems
april, 2024
Type de publication :
Article (revues avec comité de lecture)
Journal :
Stochastic Processs and Their Applications, vol. 170, pp. 104261
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Mots clés :
Weak Dirichlet processes; càdlàg semimartingales; jump processes;
martingale problem; singular drift; random measure.
Résumé :
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},
}