Weak Dirichlet processes and generalized martingale problems
soumis
Type de publication :
Article (revues avec comité de lecture)
Journal :
Preprint HAL 01241073
HAL :
arXiv :
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-2200,
author={E.lena Bandini and Francesco Russo },
title={Weak Dirichlet processes and generalized martingale problems },
journal={Preprint HAL 01241073 },
year={soumis },
}