THEORY OF ADIABATIC FLUCTUATIONS - 3RD-ORDER NOISE

We consider the response of a dynamical system driven by external adia batic fluctuations. Based on the 'adiabatic following approximation' w e have made a systematic separation of timescales to carry out an expa nsion in alpha\mu\(-1), where alpha is the strength of fluctuations an d \mu\ is the damping rate. We show that the probability distribution functions obey the differential equations of motion which contain thir d-order terms (beyond the usual Fokker-Planck terms) leading to non-Ga ussian noise. The problem of adiabatic fluctuations in velocity space which is the counterpart of Brownian motion for fast fluctuations, has been solved exactly. The characteristic function and the associated p robability distribution function are shown to be of stable form. The l inear dissipation leads to a steady state which is stable and the vari ances and higher moments are shown to be finite.