On the simulation of general tempered stable Ornstein–Uhlenbeck processes

ABSTRACT

We give an explicit representation for the transition law of a tempered stable Ornstein–Uhlenbeck process and use it to develop a rejection sampling algorithm for exact simulation of increments from this process. Our results apply to general classes of both univariate and multivariate tempered stable distributions and contain a number of previously studied results as special cases.

Keywords:

• Tempered stable distributions
• Ornstein–Uhlenbeck processes
• rejection sampling
• selfdecomposability

MSC 2010:

• 60E7
• 65C10
• 68U20

Acknowledgments

The author wishes to thank the associate editor and the anonymous referee, whose comments led to improvements in the presentation of this paper.

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This study was funded by the Russian Science Foundation (project no. 17-11-01098).