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Strong approximations and sequential change-point analysis for diffusion processes

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  • Mihalache, Stefan

Abstract

In this paper ergodic diffusion processes depending on a parameter in the drift are considered under the assumption that the processes can be observed continuously. Strong approximations by Wiener processes for a stochastic integral and for the estimator process constructed by the one-step procedure of Le Cam are obtained. Applying these approximations, a CUSUM-type procedure is developed for the sequential testing of changes in the parameter.

Suggested Citation

  • Mihalache, Stefan, 2012. "Strong approximations and sequential change-point analysis for diffusion processes," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 464-472.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:3:p:464-472
    DOI: 10.1016/j.spl.2011.11.026
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    References listed on IDEAS

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    1. Junmo Song & Sangyeol Lee, 2009. "Test for parameter change in discretely observed diffusion processes," Statistical Inference for Stochastic Processes, Springer, vol. 12(2), pages 165-183, June.
    2. Gerencsér, László, 1991. "Strong approximation of vector-valued stochastic integrals," Statistics & Probability Letters, Elsevier, vol. 12(3), pages 201-207, September.
    3. Aue, Alexander, 2004. "Strong approximation for RCA(1) time series with applications," Statistics & Probability Letters, Elsevier, vol. 68(4), pages 369-382, July.
    4. Sangyeol Lee & Yoichi Nishiyama & Nakahiro Yoshida, 2006. "Test for Parameter Change in Diffusion Processes by Cusum Statistics Based on One-step Estimators," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(2), pages 211-222, June.
    5. Aue, Alexander & Horváth, Lajos, 2004. "Delay time in sequential detection of change," Statistics & Probability Letters, Elsevier, vol. 67(3), pages 221-231, April.
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    Cited by:

    1. Koji Tsukuda, 2017. "A change detection procedure for an ergodic diffusion process," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(4), pages 833-864, August.
    2. Herold Dehling & Brice Franke & Thomas Kott & Reg Kulperger, 2014. "Change point testing for the drift parameters of a periodic mean reversion process," Statistical Inference for Stochastic Processes, Springer, vol. 17(1), pages 1-18, April.

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