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Tempered stable distributions and finite variation Ornstein-Uhlenbeck processes

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  • Nicola Cufaro Petroni
  • Piergiacomo Sabino

Abstract

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 be hereafter called the \emph{a-reminder} of their self-decomposable stationary laws. In the present study we fully characterize the L\'evy triplet of these a-reminder s and we provide a general framework to deduce the transition laws of the finite variation Ornstein-Uhlenbeck processes associated with tempered stable distributions. We focus finally on the subclass of the exponentially-modulated tempered stable laws and we derive the algorithms for an exact generation of the skeleton of Ornstein-Uhlenbeck processes related to such distributions, with the further advantage of adopting a procedure computationally more efficient than those already available in the existing literature.

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  • Nicola Cufaro Petroni & Piergiacomo Sabino, 2020. "Tempered stable distributions and finite variation Ornstein-Uhlenbeck processes," Papers 2011.09147, arXiv.org.
    • Handle: RePEc:arx:papers:2011.09147
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    References listed on IDEAS

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    Cited by:

    1. M. Gardini & P. Sabino & E. Sasso, 2021. "The Variance Gamma++ Process and Applications to Energy Markets," Papers 2106.15452, arXiv.org.

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