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

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  • Fitoussi, Mathis
  • Menozzi, Stéphane

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.

Suggested Citation

  • Fitoussi, Mathis & Menozzi, Stéphane, 2025. "Weak Error on the densities for the Euler scheme of stable additive SDEs with Hölder drift," Stochastic Processes and their Applications, Elsevier, vol. 190(C).
    • Handle: RePEc:eee:spapps:v:190:y:2025:i:c:s0304414925001796
    DOI: 10.1016/j.spa.2025.104736
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    References listed on IDEAS

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    1. Kelbert, M. & Konakov, V. & Menozzi, S., 2016. "Weak error for Continuous Time Markov Chains related to fractional in time P(I)DEs," Stochastic Processes and their Applications, Elsevier, vol. 126(4), pages 1145-1183.
    2. Remigijus Mikulevicius & Eckhard Platen, 1991. "Rate of Convergence of the Euler Approximation for Diffusion Processes," Published Paper Series 1991-3, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    3. Kulik, Alexei M., 2019. "On weak uniqueness and distributional properties of a solution to an SDE with α-stable noise," Stochastic Processes and their Applications, Elsevier, vol. 129(2), pages 473-506.
    4. Konakov Valentin & Mammen Enno, 2002. "Edgeworth type expansions for Euler schemes for stochastic differential equations," Monte Carlo Methods and Applications, De Gruyter, vol. 8(3), pages 271-286, December.
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