Article Dans Une Revue Stochastic Processes and their Applications Année : 2024

Weak error on the densities for the Euler scheme of stable additive SDEs with Hölder drift

Résumé

We are interested in the Euler-Maruyama dicretization of the SDE dXt =b(t,Xt)dt+ dZt, X0 =x∈Rd, where Zt is a symmetric isotropic d-dimensional α-stable process, α ∈ (1, 2] and the drift b ∈ L∞ ([0,T],Cβ(Rd,Rd)), β ∈ (0,1), is bounded and Hölder regular in space. Using an Euler scheme with a randomization of the time variable, we show that, denoting γ := α + β − 1, the weak error on densities related to this discretization converges at the rate γ/α.

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Dates et versions

hal-04733240 , version 1 (11-10-2024)
hal-04733240 , version 2 (03-02-2026)
hal-04733240 , version 3 (14-04-2026)

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Mathis Fitoussi, Stephane Menozzi. Weak error on the densities for the Euler scheme of stable additive SDEs with Hölder drift. Stochastic Processes and their Applications, 2024, 190, Paper 104736. ⟨10.1016/j.spa.2025.104736⟩. ⟨hal-04733240v1⟩
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