Functional Inequalities For The Generalized CIR Model

Cox-Ingersoll-Ross(CIR)model is a model of the term structure of interest rates in finance.It has important applications in many fields such as finance and biology.Therefore it is an important research topic in stochastic analysis.In this thesis,we mainly focus on the study of functional inequalities for the generalized CIR model.We mainly discuss Harnack inequality,log-Harnack inequality,the estimate of the intrinsic gradient and the super-Poincaré inequality.In Section 1,we introduce the research background of the generalized CIR model,and present the main research content and results of this article.In Section 2,we firstly introduce the definition of Harnack inequality.Then we establish Harnack inequality,log-Harnack inequality,the estimate of the intrinsic gradient by constructing the coupling by change of measure.In Section 3,we introduce the definition of super-Poincaré inequality.By using isoperimetric constant,some optimal estiamte function in the super-Poincaré inequality for the associated Dirichlet form is also obtained.