Financial models consider often stochastic processes satisfying certain differential equations. We show that the solution of a particular geometric Brownian motion observed in discrete time is asymptotically equivalent with a Gaussian white noise model.

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...