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.

We study the statistical properties of the star-shaped approximation of in vitro tumor profiles. The emphasis is on the two-point correlation structure of the radii of the tumor as a function of time and angle. In particular, we show that spatial two-point correlators follow a cosine law....

A class of new parametric models on the unit simplex in Rm is introduced, the distributions in question being obtained as conditional distributions of m independent generalized inverse Gaussian random variables given their sum. The Dirichlet model occurs as a special case. Two other special...

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 and puts in context some of our recent work on stochastic volatility (SV) modelling for financial economics. Here our main focus is on: (i) the relationship between subordination and SV, (ii) OU based volatility models, (iii) exact option pricing, (iv) realized power...

One of the difficulties that arise in the statistical analysis of autoregressive schemes is the very complex nature of the domain of the regression parameters. In the present paper we study an alternative parametrization of autoregressive models of finite order, namely the parametrization by the...

This paper proposes a reformulation and extension of the concept of Extended Self-Similarity. In support of this new hypothesis, we discuss an analysis of the probability density function (pdf) of turbulent velocity increments based on the class of normal inverse Gaussian distributions. It...

Any generalized inverse Gaussian distribution with a non-positive power parameter is shown to be the distribution of the first hitting time of level 0 for each of a variety of time-homogeneous diffusions on the interval [0, [infinity]). The infinite divisibility of the generalized inverse...