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Uniform concentration inequality for ergodic diffusion processes observed at discrete times

  • Galtchouk, L.
  • Pergamenshchikov, S.

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.

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File URL: http://www.sciencedirect.com/science/article/pii/S0304414912001974
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Article provided by Elsevier in its journal Stochastic Processes and their Applications.

Volume (Year): 123 (2013)
Issue (Month): 1 ()
Pages: 91-109

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Handle: RePEc:eee:spapps:v:123:y:2013:i:1:p:91-109
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  1. Dedecker, Jérôme & Doukhan, Paul, 2003. "A new covariance inequality and applications," Stochastic Processes and their Applications, Elsevier, vol. 106(1), pages 63-80, July.
  2. 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, 05.
  3. 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.
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