Mean relaxation time approximation for dynamical correlation functions in stochastic systems near instabilities

We present a simple approximation for dynamical correlation functions in stochastic systems which reproduces the high as well as the low frequency behaviour of the exact correlation functions. The approximation is applied in its lowest order to diffusion in a quartic potential and to autocatalytic chemical reaction systems as described by the Schlögl models. The results are compared to those from the conventional Mori-Zwanzig projection operator approach which reproduces only the short-time relaxation of the systems considered. The new approximation describes correctly slow relaxation processes, e.g. barrier crossing in a quartic potential and the slowing down of dynamic processes in finite autocatalytic systems near first and second order transitions.