On the regularity of many-particle dynamical systems perturbed by white noise

The paper considers a system of finite number of particles that ar moving in R^d under mutual interaction. It is assumed that the particles are subjected to some additional random forces which cause diffusion motion of the particles. The latter is described by a system of stochastic differential equations of the first order for noninertia particles and the second order for inertial particles. The coefficient of the system are unbounded because the interaction force tends to infinity if the distance between two particles tends to zero. The system is called regular if no particle can hit the other. The paper investigates conditions of regularity.