On maximum likelihood identification of spatially-varying parameters in stochastic parabolic systems

The maximum likelihood estimation (M.L.E.) for spatially-varying parameters in stochastic parabolic systems is studied. The main result is to show the consistency property of the M.L.E. for unknown parameters by using the method of sieves, i.e., first the admissible class of unknown parameters is projected into a finite-dimensional space and next the convergence of the derived finite-dimensional M.L.E. to the infinite-dimensional M.L.E. is justified under some conditions. Finally numerical examples are presented.