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Characterizations of Wishart Processes and Wishart Distributions

Abstract : We characterize 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. In particular, we show that the exact parameter domain of Wishart distributions equals the so-called non-central Gindikin set, which links the rank of the non-centrality parameter (resp. initial value) to the size of the shape parameter (resp. drift parameter). Our novel approach utilizes the action of Wishart semigroups on symmetric polynomials. Also, we prove a conjecture by Damir Filipovic (2009) on the existence of such semigroups on the cones of lower rank matrices.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-01342272
Contributor : Piotr Graczyk Connect in order to contact the contributor
Submitted on : Tuesday, July 5, 2016 - 4:13:34 PM
Last modification on : Monday, November 15, 2021 - 1:10:06 PM
Long-term archiving on: : Thursday, October 6, 2016 - 1:33:03 PM

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  • HAL Id : hal-01342272, version 1

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Piotr Graczyk, Jacek Malecki, Eberhard Mayerhofer. Characterizations of Wishart Processes and Wishart Distributions. 2016. ⟨hal-01342272⟩

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