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: 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.
Bandini E., Russo F. (2024). Weak Dirichlet processes and generalized martingale problems. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 170, 1-37 [10.1016/j.spa.2023.104261].
Weak Dirichlet processes and generalized martingale problems
Bandini E.
;
2024
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: 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.| File | Dimensione | Formato | |
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Bandini_Russo_WD_Final.pdf
embargo fino al 09/11/2024
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Licenza per Accesso Aperto. Creative Commons Attribuzione - Non commerciale - Non opere derivate (CCBYNCND)
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