Well-Posedness of the Second-Order SDEs Describing an N-Particle System Interacting via Coulomb Interaction

Abstract

This paper concerns a second-order N interacting stochastic particle system with singular potential for any dimension n ≥ 2. By some estimates of total energy of the system, we prove that there is no collision among particles almost surely in any finite time interval, then the well-posedness of this interacting particle system can be established.