  In this paper, we present some asymptotic properties of the normalized
inverse-Gaussian process. In particular, when the concentration parameter is
large, we establish an analogue of the empirical functional central limit
theorem, the strong law of large numbers and the Glivenko-Cantelli theorem for
the normalized inverse-Gaussian process and its corresponding quantile process.
We also derive a finite sum-representation that converges almost surely to the
Ferguson and Klass representation of the normalized inverse-Gaussian process.
This almost sure approximation can be used to simulate efficiently the
normalized inverse-Gaussian process.
