Journal of Applied Mathematics and Stochastic Analysis
Volume 9 (1996), Issue 4, Pages 427-437

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

Anatoli V. Skorokhod1,2

1Michigan State University, Department of Statistics and Probability, East Lansing 48824-1027, MI, USA
2Ukrainian Academy of Sciences, The Institute of Mathematics, Kiev, Ukraine

Received 1 May 1996; Revised 1 October 1996

Copyright © 1996 Anatoli V. Skorokhod. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider a system of finite number of particles that are moving in Rd 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. We investigate conditions of regularity.

This article is dedicated to the memory of Roland L. Dobrushin.