We consider a diffusion model of small variable type with positive drift density varying in a nonparametric set. We investigate Gaussian and Poisson approximations to this model. In the sense of asymptotic equivalence of experiments, it is shown that observation of the diffusion process until...

This paper improves previous sufficient conditions for stationarity obtained in the context of a general nonlinear vector autoregressive model with nonlinear autoregressive conditional heteroskedasticity. The results are proved by using the stability theory developed for Markov chains....