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

Yozo Tonaki (), Yusuke Kaino and Masayuki Uchida
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Yozo Tonaki: Osaka University
Yusuke Kaino: Kobe University
Masayuki Uchida: Osaka University

Metrika: International Journal for Theoretical and Applied Statistics, 2025, vol. 88, issue 5, No 2, 656 pages

Abstract: 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.

Keywords: Adaptive estimation; High frequency data; Minimum contrast estimation; Stochastic partial differential equations in two space dimensions; Thinned data (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00184-024-00969-x

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