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

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).