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A characterization of Wishart processes and Wishart distributions

Author

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  • Graczyk, Piotr
  • Małecki, Jacek
  • Mayerhofer, Eberhard

Abstract

A characterization of the existence of non-central Wishart distributions (with shape and non-centrality parameter) as well as the existence of solutions to Wishart stochastic differential equations (with initial data and drift parameter) in terms of their exact parameter domains is given. These two families are the natural extensions of the non-central chi-square distributions and the squared Bessel processes to the positive semidefinite matrices.

Suggested Citation

  • Graczyk, Piotr & Małecki, Jacek & Mayerhofer, Eberhard, 2018. "A characterization of Wishart processes and Wishart distributions," Stochastic Processes and their Applications, Elsevier, vol. 128(4), pages 1386-1404.
    • Handle: RePEc:eee:spapps:v:128:y:2018:i:4:p:1386-1404
    DOI: 10.1016/j.spa.2017.07.010
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    References listed on IDEAS

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    1. Christa Cuchiero & Josef Teichmann, 2011. "Path properties and regularity of affine processes on general state spaces," Papers 1107.1607, arXiv.org, revised Jan 2013.
    2. Letac, Gérard & Massam, Hélène, 2008. "The noncentral Wishart as an exponential family, and its moments," Journal of Multivariate Analysis, Elsevier, vol. 99(7), pages 1393-1417, August.
    3. Mayerhofer, Eberhard, 2013. "On the existence of non-central Wishart distributions," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 448-456.
    4. Christa Cuchiero & Damir Filipovi'c & Eberhard Mayerhofer & Josef Teichmann, 2009. "Affine processes on positive semidefinite matrices," Papers 0910.0137, arXiv.org, revised Apr 2011.
    5. Christa Cuchiero & Martin Keller-Ressel & Josef Teichmann, 2012. "Polynomial processes and their applications to mathematical finance," Finance and Stochastics, Springer, vol. 16(4), pages 711-740, October.
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    Cited by:

    1. Nardo, Elvira Di, 2020. "Polynomial traces and elementary symmetric functions in the latent roots of a non-central Wishart matrix," Journal of Multivariate Analysis, Elsevier, vol. 179(C).

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