Parameter estimation for a linear parabolic SPDE model in two space dimensions with a small noise

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

Statistical Inference for Stochastic Processes, 2024, vol. 27, issue 1, No 5, 123-179

Abstract: Abstract We study parameter estimation for a linear parabolic second-order stochastic partial differential equation (SPDE) in two space dimensions with a small dispersion parameter using high frequency data with respect to time and space. We set two types of Q-Wiener processes as a driving noise. We provide minimum contrast estimators of the coefficient parameters of the SPDE appearing in the eigenfunctions of the differential operator of the SPDE based on the thinned data in space, and approximate the coordinate process based on the thinned data in time. Moreover, we propose an estimator of the drift parameter using the fact that the coordinate process is the Ornstein-Uhlenbeck process and statistical inference for diffusion processes with a small noise. We also give an example and simulation results for the proposed estimators.

Keywords: Adaptive estimation; High frequency data; Small noise; Stochastic partial differential equations in two space dimensions; Q-Wiener process (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s11203-023-09301-2

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