The asymptotic dynamics of processes with multiplicative quadratic noise

The mean value of a non-Markovian stochastic process modelled by the rate equation with a multiplicative Ornstein-Uhlenbeck noise is investigated. The stability properties are discussed and the temporal evolution of the mean value and fluctuations of the process are presented. The effective relaxation time of the system is analysed.The research reported in this paper is supported in part by the Polish Academy of Sciences under the contract CPBP 1.1.4. The authors acknowledge the referee for valuable remarks.