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On the transition laws of p-tempered $$\alpha $$ α -stable OU-processes

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  • Michael Grabchak

    (University Of North Carolina Charlotte)

Abstract

We derive an explicit representation for the transition law of a p-tempered $$\alpha $$ α -stable process of Ornstein–Uhlenbeck-type and use it to develop a methodology for simulation. Our results apply in both the univariate and multivariate cases. Special attention is given to the case where $$p\le \alpha $$ p ≤ α , which is more complicated and requires developing the new class of so-called incomplete gamma distributions.

Suggested Citation

  • Michael Grabchak, 2021. "On the transition laws of p-tempered $$\alpha $$ α -stable OU-processes," Computational Statistics, Springer, vol. 36(2), pages 1415-1436, June.
    • Handle: RePEc:spr:compst:v:36:y:2021:i:2:d:10.1007_s00180-020-01055-2
    DOI: 10.1007/s00180-020-01055-2
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    References listed on IDEAS

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    1. Shibin Zhang & Xinsheng Zhang, 2008. "Exact Simulation of IG-OU Processes," Methodology and Computing in Applied Probability, Springer, vol. 10(3), pages 337-355, September.
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    4. Michael Grabchak & Gennady Samorodnitsky, 2010. "Do financial returns have finite or infinite variance? A paradox and an explanation," Quantitative Finance, Taylor & Francis Journals, vol. 10(8), pages 883-893.
    5. Bianchi, Michele Leonardo & Rachev, Svetlozar T. & Kim, Young Shin & Fabozzi, Frank J., 2011. "Tempered infinitely divisible distributions and processes," Working Paper Series in Economics 26, Karlsruhe Institute of Technology (KIT), Department of Economics and Management.
    6. Ole E. Barndorff‐Nielsen & Neil Shephard, 2001. "Non‐Gaussian Ornstein–Uhlenbeck‐based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
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