Integrated Wishart bridge processes and generalised Hartman-Watson law

TL;DR

This paper derives the joint distribution and Laplace transform of an integrated Wishart bridge process and an inverse Wishart process, advancing understanding of their probabilistic properties through bridge process analysis.

Contribution

It introduces a novel approach to analyze the joint law of Wishart and inverse Wishart bridge processes using absolute continuity and Laplace transform techniques.

Findings

Laplace transform of the joint law is explicitly obtained.

The study reveals new properties of Wishart bridge processes.

Provides tools for future probabilistic and statistical applications.

Abstract

This article is concerned with the joint law of an integrated Wishart bridge process and the trace of an integrated inverse Wishart bridge process over the interval $ \left[0,t\right] $. Its Laplace transform is obtained by studying the Wishart bridge processes and the absolute continuity property of Wishart laws.