ABSTRACT
Considering stationary diffusion models in many applications it is desirable to incorporate some of the statistical aspects of the empirical data. In Barndorff-Nielsen [1] a number of key features are formulated for observational series from finance and turbulence. In Bibby and S0rensen [5] and Rydberg [30] one-dimensional ergodic diffusions with stationary generalized hyperbolic distributions are introduced and applications to the mathematical finance are analysed. A class of ergodic diffusions with positive values, having the generalized inverse Gaussian distributions as stationary distributions was defined in Borkovec and Klüppelberg [7], where the extremal behaviour of diffusion models in finance is also investigated.
