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Local linear estimation for stochastic processes driven by $$\alpha $$ α -stable L $$\acute{\mathbf{e}}$$ e ´ vy motion

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  • Yunyan Wang
  • Lixin Zhang

Abstract

The $$\alpha $$ α -stable L $$\acute{\mathrm{e}}$$ e ´ vy motion together with the Poisson process and Brownian motion are the most important examples of L $$\acute{\mathrm{e}}$$ e ´ vy processes, which form the first class of stochastic processes being studied in the modern spirit. In this paper, the stochastic processes driven by $$\alpha $$ α -stable L $$\acute{\mathrm{e}}$$ e ´ vy motion are considered, local linear estimator of the drift function for these processes is discussed. Under mild conditions, we derive consistency of the local linear estimator of the drift function. The performance of the proposed estimator is assessed by simulation study. Copyright Springer Science+Business Media Dordrecht 2013

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sistpr:v:16:y:2013:i:2:p:161-171
    DOI: 10.1007/s11203-013-9080-3
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    References listed on IDEAS

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    1. Xu, Ke-Li, 2009. "Empirical likelihood-based inference for nonparametric recurrent diffusions," Journal of Econometrics, Elsevier, vol. 153(1), pages 65-82, November.
    2. Aleksander Janicki & Aleksander Weron, 1994. "Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes," HSC Books, Hugo Steinhaus Center, Wroclaw University of Science and Technology, number hsbook9401, December.
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    Cited by:

    1. 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.
    2. Fabian Mies & Ansgar Steland, 2019. "Nonparametric Gaussian inference for stable processes," Statistical Inference for Stochastic Processes, Springer, vol. 22(3), pages 525-555, October.

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