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<p>We study parametric estimation for second order linear parabolic stochastic partial differential equations (SPDEs) in two space dimensions driven by two types of <i>Q</i>-Wiener processes based on high frequency spatio-temporal data. First, we give estimators for damping parameters of the <i>Q</i>-Wiener processes of the SPDE using realized quadratic variations based on temporal and spatial increments. We next propose minimum contrast estimators of four coefficient parameters in the SPDE and obtain estimators of the rest of unknown parameters in the SPDE using an approximate coordinate process. We also examine numerical simulations of the proposed estimators.</p>

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Estimation for linear parabolic SPDEs in two space dimensions with unknown damping parameters

  • 期刊论文

  • 发表日期：

    2026年6月15日

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  • Yozo Tonaki,
  • Yusuke Kaino,
  • Masayuki Uchida

摘要

We study parametric estimation for second order linear parabolic stochastic partial differential equations (SPDEs) in two space dimensions driven by two types of Q-Wiener processes based on high frequency spatio-temporal data. First, we give estimators for damping parameters of the Q-Wiener processes of the SPDE using realized quadratic variations based on temporal and spatial increments. We next propose minimum contrast estimators of four coefficient parameters in the SPDE and obtain estimators of the rest of unknown parameters in the SPDE using an approximate coordinate process. We also examine numerical simulations of the proposed estimators.