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

By Igor Cialenco, Sergey V. Lototsky, Jan Pospisil. 2008

76 citations recorded by the source corpus.

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 $H\geq 1/2$. 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.

Subfields: Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6a02f939ca46bcd93f42a07bca160a32822d4b2b

How researchers see this paper

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In Finance

1. Nathan E. Glatt-Holtz
2. Igor Cialenco
3. Mathias Trabs
4. Markus Bibinger

In Mathematical Physics

1. Nathan E. Glatt-Holtz
2. Igor Cialenco

Citations in the corpus

• Parameter estimation for the stochastically perturbed Navier-Stokes equations (2010, background): “In [8, 21, 22, 30, 31], the problem has been extended to a general class of linear parabolic SPDE driven by additive noise and the convergence of the estimators has been classified in terms of the order of the corresponding differential operators.”