Maximum Likelihood Estimation Of Fast-Slow Stochastic Partial Differential Systems

In this thesis,we apply maximum likelihood estimation method to estimate the unknown parameter of a fast-slow stochastic partial differential systems with correlated noise and prove the consistency of the estimation.First,we calculate directly the maximal likelihood estimation of the unknown parameter of the fast-slow stochastic partial differential systems with correlated noise by using the Radon-Nikodym theorem.Then by finite dimensional approximation and putting the data from the fast-slow finite dimensional stochastic partial differential systems with correlated noise into the maximal likelihood estimation function,we constructed the parameter estimation of the fast-slow finite dimensional stochastic partial differential systems with correlated noise.Finally,the consistency of the parameter estimation is obtained by the approximation,and then we have the maximal likelihood estimation for the unknown parameter of the fast-slow stochastic partial differential systems with correlated noise.