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Parameter estimation for the stochastically perturbed Navier-Stokes equations

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  • Cialenco, Igor
  • Glatt-Holtz, Nathan

Abstract

We consider a parameter estimation problem of determining the viscosity [nu] of a stochastically perturbed 2D Navier-Stokes system. We derive several different classes of estimators based on the first N Fourier modes of a single sample path observed on a finite time interval. We study the consistency and asymptotic normality of these estimators. Our analysis treats strong, pathwise solutions for both the periodic and bounded domain cases in the presence of an additive white (in time) noise.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:121:y:2011:i:4:p:701-724
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    References listed on IDEAS

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    1. Lototsky, Sergey V. & Rosovskii, Boris L., 1999. "Spectral asymptotics of some functionals arising in statistical inference for SPDEs," Stochastic Processes and their Applications, Elsevier, vol. 79(1), pages 69-94, January.
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    Cited by:

    1. Cialenco, Igor & Kim, Hyun-Jung, 2022. "Parameter estimation for discretely sampled stochastic heat equation driven by space-only noise," Stochastic Processes and their Applications, Elsevier, vol. 143(C), pages 1-30.
    2. Hildebrandt, Florian & Trabs, Mathias, 2023. "Nonparametric calibration for stochastic reaction–diffusion equations based on discrete observations," Stochastic Processes and their Applications, Elsevier, vol. 162(C), pages 171-217.
    3. 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.
    4. Igor Cialenco, 2018. "Statistical inference for SPDEs: an overview," Statistical Inference for Stochastic Processes, Springer, vol. 21(2), pages 309-329, July.
    5. 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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    1. Igor Cialenco, 2018. "Statistical inference for SPDEs: an overview," Statistical Inference for Stochastic Processes, Springer, vol. 21(2), pages 309-329, July.

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