Abstract The stationary correlation function and the associated relaxation time for a general system driven by cross-correlated white noises are derived, by virtue of a Stratonovich-like ansatz. The effects of correlated noises on the relaxation time of a bistable kinetic model coupled to an additive and a multiplicative white noises are studied. It is proved that for small fluctuations the relaxation time $T_{\rm c}$ as a function of $\lambda$ (the correlated intensity between noises) exhibits very different behaviours for $\alpha < D$ and for $\alpha > D$ ($\alpha$ and $D$, respectively, stand for the ntensities of additive and multiplicative noises). When $\alpha < D$, $T_{\rm c}$ increases with increasing $\lambda$. But when $\alpha < D$, $T_{\rm c}$ increases with $\lambda$ for the case of weak correlated noises and sharply decreases with $\lambda$ for the case of strong correlated noises, and thus $T_{\rm c}$-$\lambda$ curve behaves with one extremum.
Received: 17 February 2003
Revised: 07 May 2003
Accepted manuscript online:
(Probability theory, stochastic processes, and statistics)
Fund: Project supported by the Natural Science Foundation of Yunnan Province of China (Grant No 2002A0001M) and by the Special Foundation for State Major Basic Research Program of China (Grant No 2000077602).
Cite this article:
Xie Chong-Wei (谢崇伟), Mei Dong-Cheng (梅冬成) Effects of cross-correlated noises on the relaxation time of the bistable system 2003 Chinese Physics 12 1208
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