ASYMPTOTIC PROPERTIES OF THE MAXIMUM LIKELIHOOD ESTIMATOR FOR STOCHASTIC PARABOLIC EQUATIONS WITH ADDITIVE FRACTIONAL BROWNIAN MOTION
- 1 June 2009
- journal article
- Published by World Scientific Pub Co Pte Ltd in Stochastics and Dynamics
- Vol. 9 (2), 169-185
- https://doi.org/10.1142/s0219493709002610
Abstract
A parameter estimation problem is considered for a diagonalizable 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.Keywords
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