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Trajectory fitting estimators for SPDEs driven by additive noise

Author

Listed:
  • Igor Cialenco

    (Illinois Institute of Technology)

  • Ruoting Gong

    (Illinois Institute of Technology)

  • Yicong Huang

    (Illinois Institute of Technology)

Abstract

In this paper we study the problem of estimating the drift/viscosity coefficient for a large class of linear, parabolic stochastic partial differential equations (SPDEs) driven by an additive space-time noise. We propose a new class of estimators, called trajectory fitting estimators (TFEs). The estimators are constructed by fitting the observed trajectory with an artificial one, and can be viewed as an analog to the classical least squares estimators from the time-series analysis. As in the existing literature on statistical inference for SPDEs, we take a spectral approach, and assume that we observe the first N Fourier modes of the solution, and we study the consistency and the asymptotic normality of the TFE, as $$N\rightarrow \infty $$ N → ∞ .

Suggested Citation

  • Igor Cialenco & Ruoting Gong & Yicong Huang, 2018. "Trajectory fitting estimators for SPDEs driven by additive noise," Statistical Inference for Stochastic Processes, Springer, vol. 21(1), pages 1-19, April.
    • Handle: RePEc:spr:sistpr:v:21:y:2018:i:1:d:10.1007_s11203-016-9152-2
    DOI: 10.1007/s11203-016-9152-2
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    References listed on IDEAS

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    1. Cialenco, Igor & Glatt-Holtz, Nathan, 2011. "Parameter estimation for the stochastically perturbed Navier-Stokes equations," Stochastic Processes and their Applications, Elsevier, vol. 121(4), pages 701-724, April.
    2. Cialenco, Igor & Xu, Liaosha, 2015. "Hypothesis testing for stochastic PDEs driven by additive noise," Stochastic Processes and their Applications, Elsevier, vol. 125(3), pages 819-866.
    3. Igor Cialenco & Sergey Lototsky, 2009. "Parameter estimation in diagonalizable bilinear stochastic parabolic equations," Statistical Inference for Stochastic Processes, Springer, vol. 12(3), pages 203-219, October.
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    Cited by:

    1. Bibinger, Markus & Trabs, Mathias, 2020. "Volatility estimation for stochastic PDEs using high-frequency observations," Stochastic Processes and their Applications, Elsevier, vol. 130(5), pages 3005-3052.

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