Maximum Likelihood Estimation In A Stochastic Slow-Fast System

This thesis is concerned with the maximal likelihood estimation of the unknown parameters of stochastic slow-fast partial differential system, and the consistency of the estimation.Firstly, we derive the averaged system for the stochastic slow-fast system by s-tochastic averaging principle. Further by finite dimensional approximation, the max-imal likelihood estimation of the unknown parameter of the averaged system is con-structed.Then still by finite dimensional approximation, we apply the maximal likelihood estimation for averaged equation to the stochastic slow-fast finite dimensional system. By putting the data from the stochastic slow-fast finite dimensional system and passing the approximation we have the maximal likelihood estimation for the stochastic slow-fast partial differential equations.