External noise effects on the fluctuation line width

We calculate stationary state correlation functions of the anharmonic overdamped oscillator driven by multiplicative (white Gaussian) noise of strengthQ together with additive noise of relative strengthq. (i) We donot observe a particular slowing down at the so-called noise induced transition. But there is a region of the oscillator's stiffness parametera neara0 in which the decay time is typically enhanced. (ii) If the phase transition point is defined by the minimum of the decay rate, it lies within the ordered phasea>0 forq1 and shifts down toa=0 forq0. In our approximation it is even in the disordered regiona<0 for very smallq. (iii) As a function of the multiplicative noiseQ the decay ratedecreases with increasingQ if the system is well above or well below threshold. There seem to be experimental indications of this behavior. But within the proper threshold regime of smalla increasing noiseQ increases the decay rate. The valuesa_c where the cross-over occurs depend on the fluctuating variable and onq.