Stochastic partial differential equations (SPDE) are used for
stochastic modelling, for instance, in the study of neuronal behaviour
in neurophysiology and in building stochastic models for turbulence.
Huebner, Khasminskii and Rozovskii (1993) started the investigation of
the maximum likelihood estimation of the parameters involved in two
types of SPDE's and extended their results for a class of parabolic
SPDE's in Huebner and Rozovskii (1995). Prakasa Rao (1998,2000)
obtained Bernstein - von Mises type theorems for a class of parabolic
SPDE's and investigated the properties of Bayes estimators of
parameters involved in such SPDE's. In all the papers cited earlier,
it was assumed that a continuous observation of a random field
$u_\ve(x,t)$ satisfying the SPDE over the region $[0,1] \times [0,T]$
is available. It is obvious that this assumption is not tenable in
practice and the problem of interest is to develop methods of
estimation of parameters from the random field $u_\ve(x,t)$ observed
at discrete times $t$ and at discrete positions $x$ or from the
Fourier coefficients $u_{i\ve}(t)$ observed at discrete time instants.
We construct consistent and asymptotically normal estimators of the
parameter based on the Fourier coefficients $ u_{i\ve}(t)$ observed at
discrete times $t_j = j \Dl , 0 \le j \le n$ where $\Dl >0$ and $n$
tends to infinity.