Weak Dirichlet processes and generalized martingale problems

Elena Bandini and Francesco Russo

Stochastic Processes and their Applications, 2024, vol. 170, issue C

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.

Keywords: Weak Dirichlet processes; Càdlàg semimartingales; Jump processes; Martingale problem; Singular drift; Random measure (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spa.2023.104261

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