A characterization of asymptotic behaviour of maximum likelihood estimators for stochastic PDE's
The real parameters \(\nu_1,\dots,\nu_r\) are estimated by the maximum likelihood method for the system \[ du(t,x)=\Biggl[A_0+\sum^r_{k=1}\nu_kA_k\biggr]u(t,x)dt+BdW(t,x) u(0,x)=u_0(x) \] when \(A_0,\dots,A_k\) are linear differential operators and \(W\) is a cylindrical Wiener process in \(L^2([0,T]\times G)\) \((G\subset R^d).\) Efficiency, asymptotic and consistency properties are proved.
scientific article; zbMATH DE number 1215620