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.
Weak Dirichlet processes and generalized martingale problems / Bandini E.; Russo F.. - In: STOCHASTIC PROCESSES AND THEIR APPLICATIONS. - ISSN 0304-4149. - ELETTRONICO. - 170:(2024), pp. 104261.1-104261.37. [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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