Some Properties of the Wishart Processes and a Matrix Extension of the Hartman–Watson Laws

Abstract

The aim of this paper is to discuss for Wishart processes some properties which are analogues of the corresponding well-known ones for Bessel processes. In fact, we mainly concentrate on the local absolute continuity relationship between the laws of Wishart processes with different dimensions, a property which, in the case of Bessel processes, has proven to play a rather important role in a number of applications.