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On a calculable Skorokhod’s integral based projection estimator of the drift function in fractional SDE

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  • Nicolas Marie

    (Université Paris Nanterre)

Abstract

This paper deals with a Skorokhod’s integral based projection type estimator $${\widehat{b}}_m$$ b ^ m of the drift function $$b_0$$ b 0 computed from $$N\in \mathbb N^*$$ N ∈ N ∗ independent copies $$X^1,\dots ,X^N$$ X 1 , ⋯ , X N of the solution X of $$dX_t = b_0(X_t)dt +\sigma dB_t$$ d X t = b 0 ( X t ) d t + σ d B t , where B is a fractional Brownian motion of Hurst index $$H\in (1/2,1)$$ H ∈ ( 1 / 2 , 1 ) . Skorokhod’s integral based estimators cannot be calculated directly from $$X^1,\dots ,X^N$$ X 1 , ⋯ , X N , but in this paper an $$\mathbb L^2$$ L 2 -error bound is established on a calculable approximation of $${\widehat{b}}_m$$ b ^ m .

Suggested Citation

  • Nicolas Marie, 2024. "On a calculable Skorokhod’s integral based projection estimator of the drift function in fractional SDE," Statistical Inference for Stochastic Processes, Springer, vol. 27(2), pages 391-405, July.
    • Handle: RePEc:spr:sistpr:v:27:y:2024:i:2:d:10.1007_s11203-024-09306-5
    DOI: 10.1007/s11203-024-09306-5
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    References listed on IDEAS

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    1. Andreas Neuenkirch & Samy Tindel, 2014. "A least square-type procedure for parameter estimation in stochastic differential equations with additive fractional noise," Statistical Inference for Stochastic Processes, Springer, vol. 17(1), pages 99-120, April.
    2. Fabienne Comte & Nicolas Marie, 2019. "Nonparametric estimation in fractional SDE," Statistical Inference for Stochastic Processes, Springer, vol. 22(3), pages 359-382, October.
    3. Fabienne Comte & Nicolas Marie, 2021. "Nonparametric estimation for I.I.D. paths of fractional SDE," Statistical Inference for Stochastic Processes, Springer, vol. 24(3), pages 669-705, October.
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