We consider the construction of normal inverse Gaussian (NIG) (and some related) Levy processes from the probabilistic viewpoint and from that of the theory of pseudo-differential operators; we then introduce and analyse natural generalizations of these constructions. The resulting Feller...

This paper reviews the roles of gamma type kernels in the theory and modelling for Brownian and Lévy semistationary processes. Applications to financial econometrics and the physics of turbulence are pointed out.