Characterizations of Wishart Processes and Wishart Distributions - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2016

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.
Fichier principal
Vignette du fichier
Wishart_Project11PTRF-1.pdf (319.21 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01342272 , version 1 (05-07-2016)

Identifiers

  • HAL Id : hal-01342272 , version 1

Cite

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

Share

Gmail Facebook X LinkedIn More