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<p>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 <i>Q</i>-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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年6月27日

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  • Yozo Tonaki,
  • Yusuke Kaino,
  • Masayuki Uchida

摘要

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.