A Class Of Maximum Likelihood Estimation Of Parameters In Nonlinear Stochastic Partial Differential Equations

Maximum likelihood estimation is applied to the following SPDE defined on (0,π) where 9 is an unknown parameter to be estimated and W is a Q-Wiener process valued in L2(0,π).There is no general approach to estimate parameter in SPDEs, our method is ap-plying finite dimensional approximation, that is we project the system into N dimen-sional space and give the finite dimensional maximum likelihood estimate θN which is proved to be consistency.