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Drift Estimation for Discretely Sampled SPDEs. (arXiv:1904.10884v1 [math.PR])
来源于:arXiv
The aim of this paper is to study the asymptotic properties of the maximum
likelihood estimator (MLE) of the drift coefficient for fractional stochastic
heat equation driven by an additive space-time noise. We consider the
traditional for stochastic partial differential equations statistical
experiment when the measurements are performed in the spectral domain, and in
contrast to the existing literature, we study the asymptotic properties of the
maximum likelihood (type) estimators (MLE) when both, the number of Fourier
modes and the time go to infinity. In the first part of the paper we consider
the usual setup of continuous time observations of the Fourier coefficients of
the solutions, and show that the MLE is consistent, asymptotically normal and
optimal in the mean-square sense. In the second part of the paper we
investigate the natural time discretization of the MLE, by assuming that the
first N Fourier modes are measured at M time grid points, uniformly spaced over
the time inte 查看全文>>