On some stochastic properties in Devaney’s chaos

The author complements recent results obtained by Xu et al. [Xu Z, Lin W, Ruan J. Decay of correlations implies chaos in the sense of Devaney. Chaos, Solitons & Fractals 2004;22:305–10, Wu C., Xu Z, Lin W, Ruan J. Stochastic properties in Devaney’s chaos. Chaos, Solitons & Fractals 2005;23:1195–9.] and Abraham et al. [Abraham C, Biau G, Cadre B. Chaotic properties of a mapping on a probability space. J Math Anal Appl 2002;266:420–31] on the links between several topological and stochastic properties of dynamical systems.