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.
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Acknowledgements
The authors wish to thank the referee for his/her valuable comments and suggestions. This work was partially supported by JST CREST Grant Number JPMJCR2115, MEXT Grant Number JPJ010217 and ISM Cooperative Research Program (2022-ISMCRP-1013).
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Tonaki, Y., Kaino, Y. & Uchida, M. Parametric estimation for linear parabolic SPDEs in two space dimensions based on temporal and spatial increments. Metrika (2024). https://doi.org/10.1007/s00184-024-00969-x
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DOI: https://doi.org/10.1007/s00184-024-00969-x