Parameter estimation for linear parabolic <scp>SPDEs</scp> in two space dimensions based on high frequency data

We consider parameter estimation for a linear parabolic second-order stochastic partial differential equation (SPDE) in two space dimensions driven by types of Q $$ -Wiener processes based on high frequency data time and space. first estimate the parameters which appear eigenfunctions operator SPDE using minimum contrast estimator thinned with respect to space, then construct an approximate coordinate process SPDE. Furthermore, we propose estimators coefficient utilizing time. also give some simulation results.