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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; attali@ensae.fr.
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Abstract

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

Keywords

ErgodicMarkov chainFellerQuasi-Fellerinvariant measuregeometric ergodicityrate of convergenceARCH modelsMarkov 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

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