Strong solutions to a beta-Wishart particle system
Probability
2020-03-20 v1
Abstract
The purpose of this paper is to study the existence and uniqueness of solutions to a Stochastic Differential Equation (SDE) coming from the eigenvalues of Wishart processes. The coordinates are non-negative, evolve as Cox-Ingersoll-Ross (CIR) processes and repulse each other according to a Coulombian like interaction force. We show the existence of strong and pathwise unique solutions to the system until the first multiple collision, and give a necessary and sufficient condition on the parameters of the SDE for this multiple collision not to occur in finite time.
Keywords
Cite
@article{arxiv.2003.08699,
title = {Strong solutions to a beta-Wishart particle system},
author = {Benjamin Jourdain and Ezéchiel Kahn},
journal= {arXiv preprint arXiv:2003.08699},
year = {2020}
}
Comments
33 pages