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Non parametric estimation of the diffusion coefficients of a diffusion with jumps

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  • Schmisser, Émeline

Abstract

In this article, we consider a jump diffusion process Xtt≥0, with drift function b, diffusion coefficient σ and jump coefficient ξ2. This process is observed at discrete times t=0,Δ,…,nΔ. The sampling interval Δ tends to 0 and the time interval nΔ tends to infinity. We assume that Xtt≥0 is ergodic, strictly stationary and exponentially β-mixing. We use a penalized least-square approach to compute adaptive estimators of the functions σ2+ξ2 and σ2. We provide bounds for the risks of the two estimators.

Suggested Citation

  • Schmisser, Émeline, 2019. "Non parametric estimation of the diffusion coefficients of a diffusion with jumps," Stochastic Processes and their Applications, Elsevier, vol. 129(12), pages 5364-5405.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:12:p:5364-5405
    DOI: 10.1016/j.spa.2019.03.003
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    References listed on IDEAS

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    6. Kappus, Johanna, 2014. "Adaptive nonparametric estimation for Lévy processes observed at low frequency," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 730-758.
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    Cited by:

    1. Émeline Schmisser, 2025. "Non parametric estimation of the jump coefficient of a diffusion with jumps," Statistical Inference for Stochastic Processes, Springer, vol. 28(1), pages 1-32, April.
    2. Eddy Ella-Mintsa, 2024. "Nonparametric estimation of the diffusion coefficient from i.i.d. S.D.E. paths," Statistical Inference for Stochastic Processes, Springer, vol. 27(3), pages 585-640, October.
    3. Wang, Bin & Zheng, Xu, 2022. "Testing for the presence of jump components in jump diffusion models," Journal of Econometrics, Elsevier, vol. 230(2), pages 483-509.

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