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Strong convergence rate of the Euler scheme for SDEs driven by additive rough fractional noises

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  • Huang, Chuying
  • Wang, Xu

Abstract

The strong convergence rate of the Euler scheme for stochastic differential equations driven by additive fractional Brownian motions is studied, where the fractional Brownian motion has Hurst parameter H∈(13,12) and the drift coefficient is not required to be bounded. The Malliavin calculus, the rough path theory and the 2D Young integral are utilized to overcome the difficulties caused by the low regularity of the fractional Brownian motion and the unboundedness of the drift coefficient. The Euler scheme is proved to have strong order 2H for the case that the drift coefficient has bounded derivatives up to order three and have strong order H+12 for linear cases.

Suggested Citation

  • Huang, Chuying & Wang, Xu, 2023. "Strong convergence rate of the Euler scheme for SDEs driven by additive rough fractional noises," Statistics & Probability Letters, Elsevier, vol. 194(C).
    • Handle: RePEc:eee:stapro:v:194:y:2023:i:c:s0167715222002553
    DOI: 10.1016/j.spl.2022.109742
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    References listed on IDEAS

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    1. Hong, Jialin & Huang, Chuying & Kamrani, Minoo & Wang, Xu, 2020. "Optimal strong convergence rate of a backward Euler type scheme for the Cox–Ingersoll–Ross model driven by fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 130(5), pages 2675-2692.
    2. Peter Kloeden & Andreas Neuenkirch & Raffaella Pavani, 2011. "Multilevel Monte Carlo for stochastic differential equations with additive fractional noise," Annals of Operations Research, Springer, vol. 189(1), pages 255-276, September.
    3. Song, Jian & Tindel, Samy, 2022. "Skorohod and Stratonovich integrals for controlled processes," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 569-595.
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