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Parameter estimation for linear parabolic SPDEs in two space dimensions based on high frequency data [article]

Yozo Tonaki, Yusuke Kaino, Masayuki Uchida
2022

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We consider parameter estimation for a linear parabolic second-order stochastic partial differential equation (SPDE) in two space dimensions driven by two types $Q$-Wiener processes based on high frequency data in time and space. We first estimate the parameters which appear in the coordinate process of the SPDE using the minimum contrast estimator based on the thinned data with respect to space, and then construct an approximate coordinate process of the SPDE. Furthermore, we propose
more » ... of the coefficient parameters of the SPDE utilizing the approximate coordinate process based on the thinned data with respect to time. We also give some simulation results.
doi:10.48550/arxiv.2201.09036 fatcat:rjlyyt47sbc6bp7iuop5k57nki
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Yozo Tonaki, Yusuke Kaino, Masayuki Uchida. "Parameter estimation for linear parabolic SPDEs in two space dimensions based on high frequency data." (2022)