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.
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