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By generalizing Bogolyubov's reduced description method, we suggest aformalism to derive kinetic equations for many-body dissipative systems inexternal stochastic field. As a starting point, we use a stochastic Liouvilleequation obtained from Hamilton's equations taking dissipation and stochasticperturbations into account. The Liouville equation is then averaged overrealizations of the stochastic field by an extension of the Furutsu-Novikovformula to the case of a non-Gaussian field. As the result, a generalization ofthe 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 weakinteraction between the particles and weak intensity of the field. Within thisapproximation we get the corresponding Fokker-Planck equation for the system ina non-Gaussian stochastic field. Two particular cases by assuming eitherGaussian statistics of external perturbation or homogeneity of the system arediscussed.

The BBGKY Hierarchy and Fokker-Planck Equation for Many-Body Dissipative Randomly Driven Systems