Pré-Publication, Document De Travail Année : 2025

Weak Error on the densities for the Euler scheme of stable additive SDEs with Besov drift

Résumé

We are interested in the Euler-Maruyama dicretization of the formal SDE, $dX_t=b(t,X_t)dt+dZ_t$, where $Z$ is a symmetric isotropic d dimensional stable process of index $\alpha\in (1,2)$, and $b$ is distributional. It belongs to a mix Lebesgue-Besov space. The associated parameters satisfy some constraints which guarantee weak-well posedness. Defining an appropriate Euler scheme, we obtain a convergence rate for the weak error on the densities. The rate depends on the parameters.

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Dates et versions

hal-05420798 , version 1 (17-12-2025)

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Mathis Fitoussi, Elena Issoglio, Stéphane Menozzi. Weak Error on the densities for the Euler scheme of stable additive SDEs with Besov drift. 2025. ⟨hal-05420798⟩
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