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Euler–Maruyama scheme for SDE driven by Lévy process with Hölder drift

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  • Li, Yanfang
  • Zhao, Guohuan

Abstract

This study focuses on approximating solutions to SDEs driven by Lévy processes with Hölder continuous drifts using the Euler–Maruyama scheme. We derive the Lp-error for a broad range of driven noises, including all nondegenerate α-stable processes (0<α<2).

Suggested Citation

  • Li, Yanfang & Zhao, Guohuan, 2024. "Euler–Maruyama scheme for SDE driven by Lévy process with Hölder drift," Statistics & Probability Letters, Elsevier, vol. 215(C).
  • Handle: RePEc:eee:stapro:v:215:y:2024:i:c:s0167715224001895
    DOI: 10.1016/j.spl.2024.110220
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    References listed on IDEAS

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    1. Ngo, Hoang-Long & Taguchi, Dai, 2017. "Strong convergence for the Euler–Maruyama approximation of stochastic differential equations with discontinuous coefficients," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 55-63.
    2. Jianhai Bao & Xing Huang & Chenggui Yuan, 2019. "Convergence Rate of Euler–Maruyama Scheme for SDEs with Hölder–Dini Continuous Drifts," Journal of Theoretical Probability, Springer, vol. 32(2), pages 848-871, June.
    3. Menoukeu Pamen, Olivier & Taguchi, Dai, 2017. "Strong rate of convergence for the Euler–Maruyama approximation of SDEs with Hölder continuous drift coefficient," Stochastic Processes and their Applications, Elsevier, vol. 127(8), pages 2542-2559.
    4. Kühn, Franziska & Schilling, René L., 2019. "Strong convergence of the Euler–Maruyama approximation for a class of Lévy-driven SDEs," Stochastic Processes and their Applications, Elsevier, vol. 129(8), pages 2654-2680.
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