On the existence of negative moments for some non-colliding particle systems and its application

TL;DR

This paper establishes a dimension-independent condition for the existence of negative moments in non-colliding particle systems and applies it to analyze the convergence rate of a numerical approximation scheme.

Contribution

It introduces a new sufficient condition for negative moments that does not depend on the system's dimension, improving previous results.

Findings

Negative moments exist under the new condition regardless of dimension

The convergence rate of the Euler-Maruyama scheme is quantitatively improved

Application to non-colliding particle systems demonstrates practical relevance

Abstract

We consider a class of $d$-dimensional stochastic differential equations that model a non-colliding random particle system. We provide a sufficient condition, which does not depend on the dimension $d$, for the existence of negative moments of the gap between two particles, and then apply this result to study the strong rate of convergence of the semi-implicit Euler-Maruyama approximation scheme. Our finding improves a recent result of Ngo and Taguchi (Annals of Applied Probability, 2020).