Stochastic approach and functional models in the kinetic theory of gases

The stochastic approach [1] is applied to the theory of nonequilibrum processes in a correlated and fluctuating gas with binary collisions. Markov processes are considered that make it possible to treat in a unified manner the fluctuation and dissipation properties of a nonequilibrium system when its evolution is described on space-time scales characteristic of the kinetic theory. A nonlinear stochastic equation is obtained for the singleparticle density that is suitable for describing large fluctuations in unstable and strongly correlated states of a nonequitibrium gas.