  By generalizing Bogolyubov's reduced description method, we suggest a
formalism to derive kinetic equations for many-body dissipative systems in
external stochastic field. As a starting point, we use a stochastic Liouville
equation obtained from Hamilton's equations taking dissipation and stochastic
perturbations into account. The Liouville equation is then averaged over
realizations of the stochastic field by an extension of the Furutsu-Novikov
formula to the case of a non-Gaussian field. As the result, a generalization of
the classical Bogolyubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy is derived.
In order to get a kinetic equation for the one-particle distribution function,
we use a regular cut off procedure of the BBGKY hierarchy by assuming weak
interaction between the particles and weak intensity of the field. Within this
approximation we get the corresponding Fokker-Planck equation for the system in
a non-Gaussian stochastic field. Two particular cases by assuming either
Gaussian statistics of external perturbation or homogeneity of the system are
discussed.
