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Parameter estimation for linear parabolic SPDEs in two space dimensions based on high frequency data

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  • Yozo Tonaki
  • Yusuke Kaino
  • Masayuki Uchida

Abstract

We consider parameter estimation for a linear parabolic second‐order stochastic partial differential equation (SPDE) in two space dimensions driven by two types of Q$$ Q $$‐Wiener processes based on high frequency data in time and space. We first estimate the parameters which appear in the eigenfunctions of the differential operator of the SPDE using the minimum contrast estimator based on the thinned data with respect to space, and then construct an approximate coordinate process of the SPDE. Furthermore, we propose estimators of the coefficient parameters of the SPDE utilizing the approximate coordinate process based on the thinned data with respect to time. We also give some simulation results.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:scjsta:v:50:y:2023:i:4:p:1568-1589
    DOI: 10.1111/sjos.12663
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    References listed on IDEAS

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    1. Uchida, Masayuki & Yoshida, Nakahiro, 2013. "Quasi likelihood analysis of volatility and nondegeneracy of statistical random field," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2851-2876.
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