Consider a semimartingale of the form Y_{t}=Y_0+\int _0^{t}a_{s}ds+\int _0^{t}_{s-} dW_{s}, where a is a locally bounded predictable process and (the volatility) is an adapted right - continuous process with left limits and W is a Brownian motion. We define the realised bipower variation process...

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...