Malliavin Calculus for Non-colliding Particle Systems

TL;DR

This paper applies Malliavin calculus to establish the existence and continuity of density functions for non-colliding particle systems like Dyson Brownian motion, extending mathematical understanding of these complex stochastic processes.

Contribution

It introduces a novel application of Malliavin calculus to prove density properties of non-colliding particle systems with smooth drift.

Findings

Proves existence of density functions for hyperbolic and Dyson Brownian particle systems.

Shows continuity of these density functions under certain conditions.

Extends previous results using advanced Malliavin calculus techniques.

Abstract

In this paper, we use Malliavin calculus to show the existence and continuity of density functions of $d$-dimensional non-colliding particle systems such as hyperbolic particle systems and Dyson Brownian motion with smooth drift. For this purpose, we apply results proved by Florit and Nualart (1995) and Naganuma (2013) on locally non-degenerate Wiener functionals.