Asymptotic dynamics of a system of a large number of particles described by the Kolmogorov–Feller equations

The grand statistical ensemble of a random number of particles for which the dynamics of the $n$-particle states is described by the Kolmogorov–Feller equations is considered. A BBGKY hierarchy corresponding to these equations is constructed. In the limit of a weak interaction and a large average number of particles, it is established that there is a connection between the solutions of the limiting hierarchy of equations and the solutions of the Boltzmann equation.