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

Mathis Fitoussi; Stéphane Menozzi

doi:10.1016/j.spa.2025.104736

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

Mathis Fitoussi
, Stéphane Menozzi

Université d'Evry Val d'Essonne

Research output: Contribution to journal › Article › peer-review

Abstract

We are interested in the Euler–Maruyama discretization of the SDE dX_t=b(t,X_t)dt+dZ_t,X₀=x∈R^d,where Z_t is a symmetric isotropic d-dimensional α-stable process, α∈(1,2] and the drift b∈L^∞[0,T],C^β(R^d,R^d), 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.

Original language	English
Article number	104736
Journal	Stochastic Processes and their Applications
Volume	190
DOIs	https://doi.org/10.1016/j.spa.2025.104736
Publication status	Published - 1 Dec 2025
Externally published	Yes

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title = "Weak Error on the densities for the Euler scheme of stable additive SDEs with H{\"o}lder drift",

abstract = "We are interested in the Euler{\textendash}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 H{\"o}lder 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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doi = "10.1016/j.spa.2025.104736",

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AU - Fitoussi, Mathis

AU - Menozzi, Stéphane

PY - 2025/12/1

Y1 - 2025/12/1

N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/105010701343

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DO - 10.1016/j.spa.2025.104736

M3 - Article

AN - SCOPUS:105010701343

SN - 0304-4149

VL - 190

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

M1 - 104736

ER -

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

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