Regular Article

Stationary distribution simulation of rare events under colored Gaussian noise

¹ Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an 710072, P.R. China
² MIIT Key Laboratory of Dynamics and Control of Complex Systems, Northwestern Polytechnical University, Xi’an 710072, P.R. China
³ Department of Physics, Humboldt University of Berlin, Berlin 12489, Germany
⁴ Potsdam Institute for Climate Impact Research, Potsdam 14412, Germany

^a e-mail: hsux3@nwpu.edu.cn

Received: 14 January 2019
Received in final form: 19 February 2019
Published online: 8 April 2019

Abstract

Forward flux sampling (FFS) has provided a convenient and efficient way to simulate rare events in equilibrium as well as non-equilibrium stochastic systems. In the present paper, the FFS scheme is applied to systems driven by colored Gaussian noise through enlarging the dimension to deal with the non-Markovian property. Besides, the parameters of the FFS scheme have to be reconsidered. Interestingly, by analyzing the effect of colored Gaussian noise on stationary distributions, some results are found which are clearly different from the case of Gaussian white noise excitation. We mainly found that the probability of the occurrence of rare events is inversely proportional to the correlation time. Comparing to the case of Gaussian white noise with the same intensity, the presence of colored Gaussian noise exerts a hindrance to the occurrence of rare events. Meanwhile, the FFS results show a good agreement with those from Monte Carlo simulations, even for the colored Gaussian noise case. This provides a potential insight into rare events of systems under non-white Gaussian noise via the FFS scheme.