Chen, X.Duan, J.2011-10-172011-10-172009Dynamics and Stability of Systems, 2009; 24(4):537-5461468-93671468-9375http://hdl.handle.net/2440/66776It is known by the Conley’s theorem that the chain recurrent set CR(’) of a deterministic flow’ on a compact metric space is the complement of the union of sets B(A) A, where A varies over the collection of attractors and B(A) is the basin of attraction of A. It has recently been shown that a similar decomposition result holds for random dynamical systems (RDSs) on non-compact separable complete metric spaces, but under a so-called absorbing condition. In the present article, the authors introduce a notion of random chain recurrent sets for RDSs, and then prove the random Conley’s theorem on non-compact separable complete metric spaces without the absorbing condition.en(c) 2009 Taylor & Francischain recurrent setsattractorsConley’s theoremrandom dynamical systemscocycleJournal article002011009910.1080/146893609031641732-s2.0-7044910634029102