Título: Approximations of the covariance operators of solutions of fractional elliptic SPDEs driven by Gaussian white noise
Palestrante: Alexandre de Bustamante Simas (UFPB & Kaust)
Local: Transmissão online.
Confira AQUI o link para transmissão.
Resumo: In this talk we will briefly present the model we are interested in, which is a fractional elliptic stochastic partial differential equation driven by Gaussian white noise. There is in the literature a standard way to approximate the covariance operator of the solution of such equations, the so-called rational approximation (Bolin and Kirchner, 2020), however this approach uses the solution to build such an approximation. By considering directly the covariance operator, we are able to provide a more computationally efficient approximation. We compute the rate of this approximation in terms of the Hilbert-Schmidt norm. Furthermore, we also obtain, rigorously, the rate of approximation of the so-called lumped mass method. This method is widely used by practitioners and is essential to make it computationally feasible to fit some models in spatial statistics. We obtain the rate of approximation of the lumped mass method in terms of the operator's norm as well as, under some additional restrictions, the Hilbert-Schmidt norm. Finally, we present the usage of these approximations in maximum likelihood estimation. Joint work with David Bolin and Zhen Xiong.
All the talks are held in English.
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