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Nonparametric estimation of the trend for stochastic differential equations driven by small α-stable noises

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  • Zhang, Xuekang
  • Yi, Haoran
  • Shu, Huisheng

Abstract

The present paper deals with the problem of nonparametric estimation of the trend for stochastic differential equations driven by small α-stable noises based on continuous-time observation. Under some certain conditions, we derive the uniform consistency and the rate of convergence of the nonparametric estimator. Besides, the asymptotic distribution of the estimator in our setting is shown to be a stable distribution.

Suggested Citation

  • Zhang, Xuekang & Yi, Haoran & Shu, Huisheng, 2019. "Nonparametric estimation of the trend for stochastic differential equations driven by small α-stable noises," Statistics & Probability Letters, Elsevier, vol. 151(C), pages 8-16.
    • Handle: RePEc:eee:stapro:v:151:y:2019:i:c:p:8-16
    DOI: 10.1016/j.spl.2019.03.012
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    References listed on IDEAS

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    1. Yunyan Wang & Lixin Zhang, 2013. "Local linear estimation for stochastic processes driven by $$\alpha $$ α -stable L $$\acute{\mathbf{e}}$$ e ´ vy motion," Statistical Inference for Stochastic Processes, Springer, vol. 16(2), pages 161-171, July.
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    4. Long, Hongwei & Ma, Chunhua & Shimizu, Yasutaka, 2017. "Least squares estimators for stochastic differential equations driven by small Lévy noises," Stochastic Processes and their Applications, Elsevier, vol. 127(5), pages 1475-1495.
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