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Parametric estimation for linear parabolic SPDEs in two space dimensions based on temporal and spatial increments

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Listed:
  • Yozo Tonaki

    (Osaka University
    Osaka University)

  • Yusuke Kaino

    (Kobe University)

  • Masayuki Uchida

    (Osaka University
    Osaka University
    Japan Science and Technology Agency)

Abstract

We deal with parameter estimation for linear parabolic second-order stochastic partial differential equations in two space dimensions driven by two types of Q-Wiener processes based on high frequency data with respect to time and space. We propose minimum contrast estimators of the coefficient parameters based on temporal and spatial increments, and provide adaptive estimators of the coefficient parameters based on approximate coordinate processes. We also give an example and simulation results of the proposed estimators.

Suggested Citation

  • Yozo Tonaki & Yusuke Kaino & Masayuki Uchida, 2025. "Parametric estimation for linear parabolic SPDEs in two space dimensions based on temporal and spatial increments," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 88(5), pages 601-656, July.
    • Handle: RePEc:spr:metrik:v:88:y:2025:i:5:d:10.1007_s00184-024-00969-x
    DOI: 10.1007/s00184-024-00969-x
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    References listed on IDEAS

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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.
    2. 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.
    3. Yozo Tonaki & Yusuke Kaino & Masayuki Uchida, 2023. "Parameter estimation for linear parabolic SPDEs in two space dimensions based on high frequency data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(4), pages 1568-1589, December.
    4. 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.
    5. 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.
    6. 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.
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