Nuclear Diffusion Equation The Diffusion Coefficient Is Estimated By A Time Dependent

In finance, the economic conditions change from time to time. To reflect the "time-dependent" effect of economic conditions, it is reasonable to expect that the instantaneous expected return and volatility depend on both time and price level for a given state variable when we selection models. For the inference of the models, the classical econometric model of economics set the model function according to economic theory and the data, and then estimates the parameters of the function and tests the relationship. But if the model and parameters of the assumption is not valid, it will cause errors. Non-parametric regression model gets a better fitting model results than classical assumptions model. For these reasons, it is necessary to study the nonparametric estimation problem in time dependent diffusion models.This paper studies non-parametric kernel estimates of the time-dependent diffusion equation based on the observations of discrete samples. The thesis is divided into two parts:First, we discussed the estimation of diffusion efficient. We applied the local kernel estimation on it and achieved the estimator of diffusion efficient. Furthermore we proved the asymptotic normality and consistency of it.We tested our techniques by simulating three data sets from specific models and obtained the good results and then applied it to the Shanghai A Share Index.