Limit theorem for coiuntable systems of stochastic differential equations

Abstract

We consider infinite systems of stochastic differential equations used to describe the motion of interacting particles in random media. It is assumed that mass of each particle tends to zero and the density of particles infinitely increases in a proper way. It is proved that the sequence of the corresponding measure-valued processes converges in distribution. We also prove existence and uniqueness of a strong solution for the limit equation.