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Ergodicity of a certain class of Non Feller Models: Applications to ARCH and Markov switching models

Published online by Cambridge University Press:  15 September 2004

Jean-Gabriel Attali
Jean-Gabriel Attali*
Affiliation:
ENSAE, Timbre J120, Bureau E01, 3 avenue Pierre Larousse, 92245 Malakoff Cedex, France; [email protected].
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Abstract

We provide an extension of topological methods applied to acertain class of Non Feller Models which we call Quasi-Feller. We give conditions to ensure the existence of a stationarydistribution. Finally, we strengthen the conditions to obtain apositive Harris recurrence, which in turn implies the existenceof a strong law of large numbers.

Keywords

ErgodicMarkov chainFellerQuasi-Fellerinvariantmeasuregeometric ergodicityrate of convergenceARCHmodelsMarkov switching.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 8 , August 2004 , pp. 76 - 86
Copyright
© EDP Sciences, SMAI, 2004

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References

P. Billingsley, Convergence of probability measures. John Wiley and Sons, New York (1968) 253.
M. Duflo, Méthodes Récursives Aléatoires. Techniques Stochastiques, Masson, Paris (1990) 359.
Duflo, M., Algorithmes Stochastiques. Math. Appl. 23 (1996) 319.
Harris, T.E., The existence of stationnary measures for certain markov processes. Proc. of the 3rd Berkeley Symposium on Mathematical Statistics and Probability 2 (1956) 113–124.
S.P. Meyn and R.L Tweedie, Markov Chains and Stochastic Stability. Springer-Verlag (1993) 550.
Pakes, A.G., Some conditions for ergodicity and recurrence of markov chains. Oper. Res. 17 (1969) 1048–1061. CrossRef