Nonparametric inference for stochastic diffusion models

This thesis concerns nonparametric estimation and inferences for stochastic diffusion models. Under a very general dependence structure, we construct simultaneous confidence bands for mean regression and volatility functions. The results are extended to heavy-tailed situations as well via the kernel quantile regression approach. Continuous time processes driven by Levy processes are discussed as well. Simulation studies show that our methods have good performance. Applications are made to S&P 500 index data and the foreign exchange rates between USD and Pound.