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Propriétés de mélange des processus autorégressifs polynomiaux. (Mixing properties of polynomial autoregressive processes). (French) Zbl 0706.60040
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

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
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