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.
2024
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].
Bandini E.; Russo F.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/950940
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