Multidimensional Yamada-Watanabe theorem and its applications to particle systems

TL;DR

This paper extends the Yamada-Watanabe theorem to multiple dimensions, applies it to matrix-valued particle systems like Wishart and Jacobi processes, and explores beta-versions, advancing theoretical understanding of these stochastic models.

Contribution

It introduces a multidimensional Yamada-Watanabe theorem and applies it to spectral matrix processes, including Wishart and Jacobi matrices, and their beta-versions.

Findings

Proved a multidimensional Yamada-Watanabe theorem.

Derived a spectral matrix version of the theorem.

Applied results to particle systems like Wishart and Jacobi processes.

Abstract

A multidimensional version of the Yamada-Watanabe theorem is proved. It implies a spectral matrix Yamada-Watanabe theorem. It is also applied to particle systems of squared Bessel processes, corresponding to matrix analogues of squared Bessel processes: Wishart and Jacobi matrix processes. The beta-versions of these particle systems are also considered.