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Uniform concentration inequality for ergodic diffusion processes observed at discrete times

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  • Galtchouk, L.
  • Pergamenshchikov, S.

Abstract

In this paper a concentration inequality is proved for the deviation in the ergodic theorem for diffusion processes in the case of discrete time observations. The proof is based on geometric ergodicity of diffusion processes. We consider as an application the nonparametric pointwise estimation problem of the drift coefficient when the process is observed at discrete times.

Suggested Citation

  • Galtchouk, L. & Pergamenshchikov, S., 2013. "Uniform concentration inequality for ergodic diffusion processes observed at discrete times," Stochastic Processes and their Applications, Elsevier, vol. 123(1), pages 91-109.
    • Handle: RePEc:eee:spapps:v:123:y:2013:i:1:p:91-109
    DOI: 10.1016/j.spa.2012.09.004
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    References listed on IDEAS

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    1. L. Galtchouk & S. Pergamenshchikov, 2006. "Asymptotically Efficient Sequential Kernel Estimates of the Drift Coefficient in Ergodic Diffusion Processes," Statistical Inference for Stochastic Processes, Springer, vol. 9(1), pages 1-16, May.
    2. Galtchouk, L. & Pergamenshchikov, S., 2007. "Uniform concentration inequality for ergodic diffusion processes," Stochastic Processes and their Applications, Elsevier, vol. 117(7), pages 830-839, July.
    3. L. Galtchouk & S. Pergamenshchikov, 2011. "Adaptive sequential estimation for ergodic diffusion processes in quadratic metric," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(2), pages 255-285.
    4. Dedecker, Jérôme & Doukhan, Paul, 2003. "A new covariance inequality and applications," Stochastic Processes and their Applications, Elsevier, vol. 106(1), pages 63-80, July.
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    Cited by:

    1. Leonid I. Galtchouk & Serge M. Pergamenshchikov, 2022. "Adaptive efficient analysis for big data ergodic diffusion models," Statistical Inference for Stochastic Processes, Springer, vol. 25(1), pages 127-158, April.
    2. Serguei Pergamenchtchikov & Alexander G. Tartakovsky, 2018. "Asymptotically optimal pointwise and minimax quickest change-point detection for dependent data," Statistical Inference for Stochastic Processes, Springer, vol. 21(1), pages 217-259, April.
    3. Pergamenchtchikov, Serguei M. & Tartakovsky, Alexander G. & Spivak, Valentin S., 2022. "Minimax and pointwise sequential changepoint detection and identification for general stochastic models," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    4. Pergamenchtchikov, Serguei & Tartakovsky, Alexander G., 2019. "Asymptotically optimal pointwise and minimax change-point detection for general stochastic models with a composite post-change hypothesis," Journal of Multivariate Analysis, Elsevier, vol. 174(C).

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