  The purpose of this paper is to study the existence and uniqueness of
solutions to a system of Stochastic Differential Equations (SDEs). The
coordinates are bounded by zero and one, 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 at zero or
one, and give a sufficient condition on the parameters of the SDEs for this
multiple collision not to occur in finite time.
