Herleitung kinetischer gleichungen mit dem verallgemeinerten Stratonovich-Verfahren

The kinetic equations for the 2-time conditional probability density are derived for Coulomb systems and coupled one-dimensional harmonic oscillators. The coupled oscillators are also treated exactly. The exact second central moment of the space coordinate is compared with that derived from the kinetic equation. This shows which approximations of the generalized Stratonovich method can be responsible for the possibly irreversible character of the derived kinetic equations. Using the approximation of long difference times the kinetic equations for Coulumb systems with and without homogeneous external magnetic field are transformed into the well-known Balescu-Lenard equations.