A Stein characterisation of the generalized hyperbolic distribution

The generalized hyperbolic (GH) distributions form a ve parameter family of
probability distributions that includes many standard distributions as special or
limiting cases, such as the generalized inverse Gaussian distribution, Student's t-
distribution and the variance-gamma distribution, and thus the normal, gamma
and Laplace distributions. In this paper, we consider the GH distribution in the
context of Stein's method. In particular, we obtain a Stein characterisation of
the GH distribution that leads to a Stein equation for the GH distribution. This
Stein equation reduces to the Stein equations from the current literature for the
aforementioned distributions that arise as limiting cases of the GH superclass.