# On the simulation of general tempered stable Ornstein–Uhlenbeck processes

@article{Grabchak2019OnTS, title={On the simulation of general tempered stable Ornstein–Uhlenbeck processes}, author={Michael Grabchak}, journal={Journal of Statistical Computation and Simulation}, year={2019}, volume={90}, pages={1057 - 1081} }

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.

## 14 Citations

### On the transition laws of p -tempered ˛ -stable OU-processes

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We develop efﬁcient methods for simulating processes of Ornstein–Uhlenbeck type related to the class of p -tempered α -stable (TS p α ) distributions. Our results hold for both the univariate and…

### Tempered stable distributions and finite variation Ornstein-Uhlenbeck processes

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Constructing \Levy-driven Ornstein-Uhlenbeck processes is a task closely related to the notion of self-decomposability. In particular, their transition laws are linked to the properties of what will…

### Exact simulation of normal tempered stable processes of OU type with applications

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We study the Ornstein-Uhlenbeck process having a symmetric normal tempered stable stationary law and represent its transition distribution in terms of the sum of independent laws. In addition, we…

### Gamma-related Ornstein–Uhlenbeck processes and their simulation*

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ABSTRACT We investigate the distributional properties of two Lévy-driven Ornstein–Uhlenbeck (OU) processes whose stationary distributions are the gamma law and the bilateral gamma law, respectively.…

### Discrete Tempered Stable Distributions

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Discrete tempered stable distributions are a large and flexible class of models for heavy tailed and overdispersed count data. In this paper we derive various properties of these distributions and…

### Discrete Tempered Stable Distributions

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Discrete tempered stable distributions are a large and flexible class of models for heavy tailed and overdispersed count data. In this paper we derive various properties of these distributions and…

### PR ] 1 8 N ov 2 02 0 Tempered stable distributions and finite variation Ornstein-Uhlenbeck processes ∗

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Constructing Lévy-driven Ornstein-Uhlenbeck processes is a task closely related to the notion of self-decomposability. In particular, their transition laws are linked to the properties of what will…

### Fast simulation of tempered stable Ornstein–Uhlenbeck processes

- MathematicsComputational Statistics
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Constructing Lévy-driven Ornstein–Uhlenbeck processes is a task closely related to the notion of self-decomposability. In particular, their transition laws are linked to the properties of what will…

### Calibration for multivariate Lévy-driven Ornstein-Uhlenbeck processes with applications to weak subordination

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Consider a multivariate Lévy-driven Ornstein-Uhlenbeck process where the stationary distribution or background driving Lévy process is from a parametric family. We derive the likelihood function…

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