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Preprints, Working Papers, ... Year : 2023

Characteristics and Itô's formula for weak Dirichlet processes: an equivalence result

Abstract

The main objective consists in generalizing a well-known Itô formula of J. Jacod and A. Shiryaev: given a càdlàg process S, there is an equivalence between the fact that S is a semimartingale with given characteristics (B^k , C, ν) and a Itô formula type expansion of F (S), where F is a bounded function of class C2. This result connects weak solutions of path-dependent SDEs and related martingale problems. We extend this to the case when S is a weak Dirichlet process. A second aspect of the paper consists in discussing some untreated features of stochastic calculus for finite quadratic variation processes.
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Dates and versions

hal-04019358 , version 1 (08-03-2023)

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  • HAL Id : hal-04019358 , version 1

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Elena Bandini, Francesco Russo. Characteristics and Itô's formula for weak Dirichlet processes: an equivalence result. 2023. ⟨hal-04019358⟩
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