A characterization of Wishart processes and Wishart distributions

Piotr Graczyk; Jacek Małecki; Eberhard Mayerhofer

doi:10.1016/j.spa.2017.07.010

A characterization of Wishart processes and Wishart distributions

Piotr Graczyk, Jacek Małecki, Eberhard Mayerhofer

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	1386-1404
Number of pages	19
Journal	Stochastic Processes and their Applications
Volume	128
Issue number	4
DOIs	https://doi.org/10.1016/j.spa.2017.07.010
Publication status	Published - Apr 2018

Keywords

Affine processes
Gindikin set
Non-central Wishart distribution
Symmetric polynomials
Wishart distributions
Wishart processes

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10.1016/j.spa.2017.07.010

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title = "A characterization of Wishart processes and Wishart distributions",

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.",

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author = "Piotr Graczyk and Jacek Ma{\l}ecki and Eberhard Mayerhofer",

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AU - Graczyk, Piotr

AU - Małecki, Jacek

AU - Mayerhofer, Eberhard

PY - 2018/4

Y1 - 2018/4

N2 - 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.

AB - 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.

KW - Affine processes

KW - Gindikin set

KW - Non-central Wishart distribution

KW - Symmetric polynomials

KW - Wishart distributions

KW - Wishart processes

UR - https://www.scopus.com/pages/publications/85027712310

U2 - 10.1016/j.spa.2017.07.010

DO - 10.1016/j.spa.2017.07.010

M3 - Article

AN - SCOPUS:85027712310

SN - 0304-4149

VL - 128

SP - 1386

EP - 1404

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 4

ER -

A characterization of Wishart processes and Wishart distributions

Abstract

Keywords

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