Journal
MONTE CARLO METHODS AND APPLICATIONS
Volume 17, Issue 3, Pages 279-300Publisher
WALTER DE GRUYTER GMBH
DOI: 10.1515/MCMA.2011.012
Keywords
Acceptance-rejection sampling; high-frequency sampling; Levy process; Ornstein-Uhlenbeck process; subordinator; transition probability; tempered stable process
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Funding
- Grants-in-Aid for Scientific Research [23300106, 21340024, 23740082] Funding Source: KAKEN
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Exact yet simple simulation algorithms are developed for a wide class of Ornstein-Uhlenbeck processes with tempered stable stationary distribution of finite variation with the help of their exact transition probability between consecutive time points. Random elements involved can be divided into independent tempered stable and compound Poisson distributions, each of which can be simulated in the exact sense through acceptance-rejection sampling, respectively, with stable and gamma proposal distributions. We discuss various alternative simulation methods within our algorithms on the basis of acceptance rate in acceptance-rejection sampling for both high-and low-frequency sampling. Numerical results illustrate their advantage relative to the existing approximative simulation method based on infinite shot noise series representation.
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