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On Lévy Semistationary Processes with a Gamma Kernel

  • Conference paper
XI Symposium on Probability and Stochastic Processes

Part of the book series: Progress in Probability ((PRPR,volume 69))

Abstract

This paper studies some probabilistic properties of a Lévy semistationary process when the kernel is given by \(\varphi _{\alpha,\lambda }\left (s\right ) = e^{-\lambda s}s^{\alpha }\) for α > −1 and λ > 0. We study the stationary distribution induced by this process. In particular, we show that this distribution is self-decomposable for − 1 < α < 0 and under certain conditions it can be characterized by the so-called cancellation property.

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Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, Aarhus University, Aarhus, Denmark

    Jan Pedersen

  2. Department of Economics and CREATES, Aarhus University, Aarhus, Denmark

    Orimar Sauri

Authors
  1. Jan Pedersen
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  2. Orimar Sauri
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Corresponding author

Correspondence to Orimar Sauri .

Editor information

Editors and Affiliations

  1. Probabilidad y Estadística, IIMAS UNAM, Mexico

    Ramsés H. Mena

  2. CIMAT, Guanajuato, Mexico

    Juan Carlos Pardo

  3. CIMAT, Guanajuato, Mexico

    Víctor Rivero

  4. Instituto de Matemáticas, UNAM, Mexico

    Gerónimo Uribe Bravo

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Pedersen, J., Sauri, O. (2015). On Lévy Semistationary Processes with a Gamma Kernel. In: Mena, R., Pardo, J., Rivero, V., Uribe Bravo, G. (eds) XI Symposium on Probability and Stochastic Processes. Progress in Probability, vol 69. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-13984-5_11

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