Abstract
We obtain geometric ergodicity and recurrence properties for the Markov chain (Xt), defined by Xt+1=φ (Xt, ut+1) where φ is a rational application and (ut) is a sequence of independent identically distributed random variables.
Preview
Unable to display preview. Download preview PDF.
Références
H. AKAIKE, Markovian representation of stochastic processes, Ann. Inst Stat. Math, 26, 1974, 363–387.
J. BOCHNAK, M. COSTE, M.F. ROY, Géométrie algèbrique réelle, Springer Verlag, Berlin, 1987
Th. BRÖCKER, Differentiable germs and catastrophes. Cambridge University Press, 1975.
J. DIEUDONNE, Eléments d'analyse, t.3, Gauthier Villars, Paris 1979.
S. LOJASIEWICZ, Ensembles semi analytiques, Multigraphie de l'I.H.E.S., Bures Sur Yvette, 1965.
A. MOKKADEM, Thèse de doctorat d'état, Orsay, 1987.
A. MOKKADEM, Sur le mélange des processus ARMA vectoriel, CRAS, t303, 519–521, 1986.
E. NUMMELIN, P. TUOMINEN, Geometric ergodicity of Harris recurrent Markov chain, Stoch. Proc. Appl., 12, 187–202, 1982.
T.D. PHAM, Bilinear markovian representation and bilinear models, Stoch. Proc. Appl., 20, 295–306, 1985.
D. REVUZ, Markov chains, Nort Holland, Amsterdam, 1984.
E.D. SONTAG, Polynomial Response Maps, Lecture Notes in Control and Information Sciences, 13, 1979.
T. SUBBA RAO, M.M. GABR, An introduction to bispectral analysis and bilinear time series models, Lect. Notes in Statistics, 24, 1984.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1989 Springer-Verlag
About this paper
Cite this paper
Mokkadem, A. (1989). Ergodicite des systems stochastiques polynomiaux en temps discret. In: Descusse, J., Fliess, M., Isidori, A., Leborgne, D. (eds) New Trends in Nonlinear Control Theory. Lecture Notes in Control and Information Sciences, vol 122. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0043047
Download citation
DOI: https://doi.org/10.1007/BFb0043047
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-51075-8
Online ISBN: 978-3-540-46143-2
eBook Packages: Springer Book Archive