Mokkadem, Abdelkader Propriétés de mélange des processus autorégressifs polynomiaux. (Mixing properties of polynomial autoregressive processes). (French) Zbl 0706.60040 Ann. Inst. Henri Poincaré, Probab. Stat. 26, No. 2, 219-260 (1990). The mixing and the ergodicity of a Markov-chain \((Z_ n)\) is studied. A continuity theorem for the image of a measure by a polynomial application is proved. Using this result, simple sufficient conditions for the chain \((Z_ n)\) to be Harris recurrent, geometrically ergodic and geometrically absolutely regular are obtained. The last part contains applications of the results to the ARMA processes and the bilinear processes. Reviewer: I.Valusescu Cited in 30 Documents MSC: 60G10 Stationary stochastic processes 60J27 Continuous-time Markov processes on discrete state spaces 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 60G99 Stochastic processes Keywords:mixing properties; polynomial autoregressive processes; continuity theorem; image of a measure; Harris recurrent; geometrically ergodic; geometrically absolutely regular; ARMA processes; bilinear processes PDF BibTeX XML Cite \textit{A. Mokkadem}, Ann. Inst. Henri Poincaré, Probab. Stat. 26, No. 2, 219--260 (1990; Zbl 0706.60040) Full Text: Numdam EuDML