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On the Euler–Maruyama scheme for spectrally one-sided Lévy driven SDEs with Hölder continuous coefficients

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  • Li, Libo
  • Taguchi, Dai

Abstract

We study in this article the strong rate of convergence of the Euler–Maruyama scheme and associated with the jump-type equation introduced in Li and Mytnik (2011). We obtain the strong rate of convergence under similar assumptions for strong existence and pathwise uniqueness. Models of this type can be considered as a generalization of the CIR (Cox–Ingersoll–Ross) process with jumps.

Suggested Citation

  • Li, Libo & Taguchi, Dai, 2019. "On the Euler–Maruyama scheme for spectrally one-sided Lévy driven SDEs with Hölder continuous coefficients," Statistics & Probability Letters, Elsevier, vol. 146(C), pages 15-26.
    • Handle: RePEc:eee:stapro:v:146:y:2019:i:c:p:15-26
    DOI: 10.1016/j.spl.2018.10.017
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    References listed on IDEAS

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    1. Mikulevicius, Remigijus & Zhang, Changyong, 2011. "On the rate of convergence of weak Euler approximation for nondegenerate SDEs driven by Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 121(8), pages 1720-1748, August.
    2. Ying Jiao & Chunhua Ma & Simone Scotti, 2017. "Alpha-CIR model with branching processes in sovereign interest rate modeling," Finance and Stochastics, Springer, vol. 21(3), pages 789-813, July.
    3. Ying Jiao & Chunhua Ma & Simone Scotti, 2017. "Alpha-CIR Model with Branching Processes in Sovereign Interest Rate Modelling," Post-Print hal-01275397, HAL.
    4. Fu, Zongfei & Li, Zenghu, 2010. "Stochastic equations of non-negative processes with jumps," Stochastic Processes and their Applications, Elsevier, vol. 120(3), pages 306-330, March.
    5. 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.
    6. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
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