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

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 prov...

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Published in:arXiv.org 2022-06
Main Authors: Tonaki, Yozo, Kaino, Yusuke, Uchida, Masayuki
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Language:English
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Ornstein-Uhlenbeck process
Parameter estimation
Partial differential equations
Statistical inference
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Kaino, Yusuke
Uchida, Masayuki
description 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 coordinate process 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.
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subjects Ornstein-Uhlenbeck process
Parameter estimation
Partial differential equations
Statistical inference
title Parameter estimation for a linear parabolic SPDE model in two space dimensions with a small noise
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