A Characterization of Wishart Processes and Wishart Distributions

TL;DR

This paper characterizes the conditions under which non-central Wishart distributions and Wishart stochastic differential equations exist, extending classical distributions and processes to the matrix setting.

Contribution

It provides a precise characterization of the parameter domains for non-central Wishart distributions and Wishart SDE solutions, advancing understanding of matrix-valued stochastic processes.

Findings

Identifies parameter conditions for Wishart distribution existence

Establishes existence criteria for Wishart SDE solutions

Extends classical distributions to matrix-valued cases

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.