First hitting time models for the generalized inverse Gaussian distribution

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 Gaussian distributions is a simple consequence of this and an elementary convolution formula for these distributions.

Finite-dimensional algebraic representations of the infinite phylon group

The concept of phylon is introduced as a generalisation of derivative strings, differential strings and new tensors. The behaviour of phyla under change of coordinates is given by finite-dimensional algebraic representations of a very large group, the infinite phylon group. These representations are studied from both the general and the matrix points of view. Various examples of phyla are given, mainly from a statistical context. The basic structure of these representations is given.</p

Finite-dimensional algebraic representations of the infinite phylon group

The concept of phylon is introduced as a generalisation of derivative strings, differential strings and new tensors. The behaviour of phyla under change of coordinates is given by finite-dimensional algebraic representations of a very large group, the infinite phylon group. These representations are studied from both the general and the matrix points of view. Various examples of phyla are given, mainly from a statistical context. The basic structure of these representations is given.</p