Parameter Estimation For Some Non-linear Diffusion Processes

This paper considers parameter estimation for diffusion processes. For linear diffusion processes, we first introduce parameter estimation for two classes of the famous model,Vasicek model and CIR model. We also present parameter estimation for another linear diffusion process, Brennan-Schwartz model. For non-linear diffusion processes we give the necessary and sufficient condition which a non-linear diffusion process can be reduced to Vasicek,CIR and Brennan-Schwartz models. Finally, we apply our results to some famous non-linear diffusion processes, including Gompertz, Rayleigh and Logistic models.