The Bogolyubov-Born-Green-Kirkwood-Yvon hierarchy and Fokker-Planck equation for many-body dissipative randomly driven systems

@article{Sliusarenko2014TheBH,
  title={The Bogolyubov-Born-Green-Kirkwood-Yvon hierarchy and Fokker-Planck equation for many-body dissipative randomly driven systems},
  author={Oleksii Sliusarenko and Alexei Chechkin and Yu. V. Slyusarenko},
  journal={Journal of Mathematical Physics},
  year={2014},
  volume={56},
  pages={043302}
}
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… 

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