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Methodology and Computing in Applied Probability

, Volume 13, Issue 3, pp 619–656 | Cite as

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

  • Shibin Zhang
Article

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.

Keywords

Self-decomposability Generalized inverse Gaussian Ornstein–Uhlenbeck Random sample generation Estimation 

AMS 2000 Subject Classifications

60E07 62E15 65C10 62M05 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of MathematicsShanghai Maritime UniversityShanghaiChina

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