With the aim of modelling key stylized features of observational series from finance and turbulence a number of stochastic processes with normal inverse Gaussian marginals and various types of dependence structures are discussed. Ornstein - Uhlenbeck type processes, superpositions of such...

We introduce a notion of volatility uncertainty in discrete time and define the corresponding analogue of Pengs G-expectation. In the continuous-time limit, the resulting sublinear expectation converges weakly to the G-expectation. This can be seen as a Donsker-type result for the G-Brownian...