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Small diffusivity asymptotics for a linear parabolic SPDE in two space dimensions

Author

Listed:
  • Yozo Tonaki

    (The University of Osaka
    The University of Osaka)

  • Yusuke Kaino

    (Kobe University)

  • Masayuki Uchida

    (The University of Osaka
    The University of Osaka
    Japan Science and Technology Agency)

Abstract

We consider parameter estimation of the reaction term for a second order linear parabolic stochastic partial differential equation in two space dimensions driven by a Q-Wiener process under small diffusivity. We first construct an estimator of the reaction parameter based on continuous spatio-temporal data, and then derive an estimator of the reaction parameter based on high frequency spatio-temporal data by discretizing the estimator based on the continuous data. We show that the estimators have consistency and asymptotic normality. Furthermore, we give simulation results of the estimator based on high frequency data.

Suggested Citation

  • Yozo Tonaki & Yusuke Kaino & Masayuki Uchida, 2025. "Small diffusivity asymptotics for a linear parabolic SPDE in two space dimensions," Statistical Inference for Stochastic Processes, Springer, vol. 28(2), pages 1-46, August.
    • Handle: RePEc:spr:sistpr:v:28:y:2025:i:2:d:10.1007_s11203-025-09330-z
    DOI: 10.1007/s11203-025-09330-z
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    References listed on IDEAS

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    1. Patrick Bossert, 2024. "Parameter estimation for second-order SPDEs in multiple space dimensions," Statistical Inference for Stochastic Processes, Springer, vol. 27(3), pages 485-583, October.
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    4. 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.
    5. 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.
    6. 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.
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