  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.
