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A note on Marked Point Processes and multivariate subordination

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  • Jevtić, Petar
  • Marena, Marina
  • Semeraro, Patrizia

Abstract

The aim of this paper is to state a correspondence between marked Poisson processes and multivariate subordinated Lévy processes. We prove that, under suitable conditions, marked Poisson processes are in law subordinated Brownian motions and we provide their Lévy triplet and characteristic function. We introduce the class of multivariate Gaussian marked Poisson processes and prove that–in law–they are multivariate subordinated Brownian motions.

Suggested Citation

  • Jevtić, Petar & Marena, Marina & Semeraro, Patrizia, 2017. "A note on Marked Point Processes and multivariate subordination," Statistics & Probability Letters, Elsevier, vol. 122(C), pages 162-167.
    • Handle: RePEc:eee:stapro:v:122:y:2017:i:c:p:162-167
    DOI: 10.1016/j.spl.2016.11.008
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    References listed on IDEAS

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    1. Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," The Journal of Business, University of Chicago Press, vol. 63(4), pages 511-524, October.
    2. Patrizia Semeraro, 2008. "A Multivariate Variance Gamma Model For Financial Applications," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(01), pages 1-18.
    3. Kozubowski, Tomasz J. & Podgórski, Krzysztof & Rychlik, Igor, 2013. "Multivariate generalized Laplace distribution and related random fields," Journal of Multivariate Analysis, Elsevier, vol. 113(C), pages 59-72.
    4. Sato, Ken-iti, 2001. "Subordination and self-decomposability," Statistics & Probability Letters, Elsevier, vol. 54(3), pages 317-324, October.
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    Cited by:

    1. Petar Jevtić & Marina Marena & Patrizia Semeraro, 2019. "Multivariate Marked Poisson Processes And Market Related Multidimensional Information Flows," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(02), pages 1-26, March.

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