Properties of noise correlation functions of langevin-like equations

The stochastic properties of the noise in Langevin type equations are studied. It is demonstrated that the noise is non-Gaussian and that the three point noise correlation function has an exponential decay on the slow time scale. Explicit calculations for systems containing one slow linear variable are carried out using mode-coupling techniques. The results are easily extended to four and higher order correlation functions and to systems in which there is more than one slow linear variable. In particular, the noise in the hydrodynamic Langevin equations has the properties described above.