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Adaptative design for estimation of parameter of second order differential equation in fractional diffusion system

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  • Cai, Chunhao
  • Lv, Wujun

Abstract

We consider a controlled second order differential equation which is partially observed with an additional fractional noise. We study the asymptotic (for large observation time) design problem of the input and give an efficient estimator of the unknown signal drift parameter. When the input depends on the unknown parameter, we will try the one-step estimation procedure using the Newton–Raphson method.

Suggested Citation

  • Cai, Chunhao & Lv, Wujun, 2020. "Adaptative design for estimation of parameter of second order differential equation in fractional diffusion system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
    • Handle: RePEc:eee:phsmap:v:541:y:2020:i:c:s0378437119319752
    DOI: 10.1016/j.physa.2019.123544
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    References listed on IDEAS

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    1. M.L. Kleptsyna & A. Le Breton, 2002. "Extension of the Kalman–Bucy Filter to Elementary Linear Systems with Fractional Brownian Noises," Statistical Inference for Stochastic Processes, Springer, vol. 5(3), pages 249-271, October.
    2. Alexandre Brouste & Marina Kleptsyna & Alexandre Popier, 2012. "Design for estimation of the drift parameter in fractional diffusion systems," Statistical Inference for Stochastic Processes, Springer, vol. 15(2), pages 133-149, July.
    3. Jean-François Coeurjolly, 2001. "Estimating the Parameters of a Fractional Brownian Motion by Discrete Variations of its Sample Paths," Statistical Inference for Stochastic Processes, Springer, vol. 4(2), pages 199-227, May.
    4. Alexandre Brouste & Marina Kleptsyna, 2010. "Asymptotic properties of MLE for partially observed fractional diffusion system," Statistical Inference for Stochastic Processes, Springer, vol. 13(1), pages 1-13, April.
    5. M.L. Kleptsyna & A. Le Breton, 2002. "Statistical Analysis of the Fractional Ornstein–Uhlenbeck Type Process," Statistical Inference for Stochastic Processes, Springer, vol. 5(3), pages 229-248, October.
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