Limit Theorem for Countable Systems of Stochastic Differential Equations

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