On the regularity of many-particle dynamical systems perturbed by white noise. (1996)

• Record Type: Journal Article
• Authors: Skorokhod, Anatoli V.
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 9:Number 4(1996)
• Page Start: 427
• Page End: 437
• Publication Date: 1996
• Subjects: many-particle systems -- inertia particle -- noninertia particle -- stochastic differential equations -- martingale -- stopping time -- regularity -- irregularity; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S1048953396000378
• Languages: English
• ISSNs: 1048-9533

Abstract

Abstract : We consider a system of finite number of particles that are 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. We investigate conditions of regularity. This article is dedicated to the memory of Roland L. Dobrushin.