Asymptotic Properties of the Maximum Likelihood Estimator for Stochastic Parabolic Equations with Additive Fractional Brownian Motion

2008/04/02 by Igor Cialenco, Cialenco, Igor, Sergey Lototsky +3
Mathematics · #60H15 #62F12 #FOS: Mathematics #Probability (math.PR) #Statistics Theory (math.ST) #math.PR #math.ST #msc:60H15 #msc:62F12 #stat.TH

paper · pdf · doi:10.48550/arxiv.0804.0407

arxiv created 2008/04/02 · arxiv updated 2009/12/01

Abstract

A parameter estimation problem is considered for a diagonaliazable stochastic evolution equation using a finite number of the Fourier coefficients of the solution. The equation is driven by additive noise that is white in space and fractional in time with the Hurst parameter H≥ 1/2. The objective is to study asymptotic properties of the maximum likelihood estimator as the number of the Fourier coefficients increases. A necessary and sufficient condition for consistency and asymptotic normality is presented in terms of the eigenvalues of the operators in the equation.

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