| Issue |
ESAIM: PS
Volume 8, August 2004
|
|
|---|---|---|
| Page(s) | 76 - 86 | |
| DOI | https://doi.org/10.1051/ps:2004003 | |
| Published online | 15 September 2004 | |
Ergodicity of a certain class of Non Feller Models: Applications to ARCH and Markov switching models
ENSAE, Timbre J120, Bureau E01, 3 avenue Pierre
Larousse, 92245 Malakoff Cedex, France; attali@ensae.fr.
Received:
7
November
2002
Revised:
12
June
2003
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.
Mathematics Subject Classification: 60B05 / 60B10 / 60J10
Key words: Ergodic / Markov chain / Feller / Quasi-Feller / invariant measure / geometric ergodicity / rate of convergence / ARCH models / Markov switching.
© EDP Sciences, SMAI, 2004
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