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

Mathis Fitoussi and Stéphane Menozzi

Stochastic Processes and their Applications, 2025, vol. 190, issue C

Abstract: We are interested in the Euler–Maruyama discretization 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.

Date: 2025
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DOI: 10.1016/j.spa.2025.104736

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