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

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

Statistical Inference for Stochastic Processes, 2025, vol. 28, issue 2, No 4, 46 pages

Abstract: Abstract 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.

Keywords: High frequency data; Linear parabolic stochastic partial differential equations; Parametric estimation; Reaction parameter; Small diffusive parameter (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s11203-025-09330-z

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