Abstract
The methods of the functional calculus are applied to the Klimontovich equation and to the Vlasov equations. The equation for the generating functional is derived for both cases. By taking moments of these equations, the BBGKY hierarchy is obtained for the case of the Klimontovich equation, and a similar hierarchy is obtained for the case of the Vlasov equation. The two hierarchies are identical, except for some terms involving individual particle interactions. Methods of solving the Vlasov hierarchy are discussed and it is shown how quasi-linear theory can be obtained.
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