Hypothesis Testing Of Maximum Likelihood Estimation For Stochastic PDE

With the improvement of the theory of stochastic analysis,stochastic partial d-ifferential equations(SPDEs)have been rapidly developed due to their wide range of applications.However,scholars pay more attention to the various parameter estimation problems of SPDEs statistical inference and few to the hypothesis testing of the equa-tions,especially of the nonlinear equations.Therefore,the hypothesis testing problem for the parameter estimation for a class of nonlinear SPDE driven by additive noise is studied.This paper consists of four parts.The first chapter explains the current research background in this field,and the significance and main work of this paper are intro-duced.The second chapter is the supplement of the preparatory knowledge.The latter reasoning is mainly based on the basic knowledge of stochastic partial differential and hypothesis testing.The third chapter discusses the boundedness of the solution of the objective equation in different senses.Moreover,in the fourth chapter,the explicit expressions for rejection domain of the unknown parameter in two asymptotic cases:T?? with N fixed and N?? with T fixed are shown and their asymptotic properties are further proved.