Transition Law-based Simulation of Generalized Inverse Gaussian Ornstein–Uhlenbeck Processes

http://www.springerlink.com/content/y32g837314576106/?p=a99bc407fe2346fabfa0b76df11506d2&pi=0

Abstract  

In this paper, a stochastic integral of Ornstein–Uhlenbeck type is
represented to be the sum of three independent random variables—one
follows a distribution whose density is a deconvolution of the
densities of two generalized inverse Gaussian distributions, and the
two others all have compound Poisson distributions. Based on the
representation of the stochastic integral, a simulation procedure for
obtaining discretely observed values of Ornstein–Uhlenbeck processes
with given generalized inverse Gaussian distribution is provided. For
some subclasses of the generalized inverse Gaussian Ornstein–Uhlenbeck
process, the innovations can be sampled exactly. The performance of the
simulation method is evidenced by some empirical results.