On random fields corresponding to the Bogolyubov, Vlasov and Boltzmann chains

The correspondence between the creation-annihilation operators for Bogolyubov and Boltzmann chains and the transforms of measures of random fields connected with the chains is established. Instead of the Bogolyubov equation in terms of the variational derivatives the equations for characteristic functionals for the momentum functional of the chains are introduced which are infinite-dimensional Fourier-transforms of the measures satisfying the analogues of the Vlassov and Kolmogorov-Feller equations. These equations are written down in terms of creation-annihilation operators acting on measures in functional spaces