# Ergodicity of a certain class of non Feller models : applications to $\mathrm{\mathit{A}\mathit{R}\mathit{C}\mathit{H}}$ and Markov switching models

ESAIM: Probability and Statistics (2004)

- Volume: 8, page 76-86
- ISSN: 1292-8100

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topAttali, Jean-Gabriel. "Ergodicity of a certain class of non Feller models : applications to $\textit {ARCH}$ and Markov switching models." ESAIM: Probability and Statistics 8 (2004): 76-86. <http://eudml.org/doc/245678>.

@article{Attali2004,

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.},

author = {Attali, Jean-Gabriel},

journal = {ESAIM: Probability and Statistics},

keywords = {ergodic; Markov chain; Feller; quasi-Feller; invariant measure; geometric ergodicity; rate of convergence; $ARCH$ models; Markov switching; Ergodic; Quasi-Feller; ARCH models},

language = {eng},

pages = {76-86},

publisher = {EDP-Sciences},

title = {Ergodicity of a certain class of non Feller models : applications to $\textit \{ARCH\}$ and Markov switching models},

url = {http://eudml.org/doc/245678},

volume = {8},

year = {2004},

}

TY - JOUR

AU - Attali, Jean-Gabriel

TI - Ergodicity of a certain class of non Feller models : applications to $\textit {ARCH}$ and Markov switching models

JO - ESAIM: Probability and Statistics

PY - 2004

PB - EDP-Sciences

VL - 8

SP - 76

EP - 86

AB - 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.

LA - eng

KW - ergodic; Markov chain; Feller; quasi-Feller; invariant measure; geometric ergodicity; rate of convergence; $ARCH$ models; Markov switching; Ergodic; Quasi-Feller; ARCH models

UR - http://eudml.org/doc/245678

ER -

## References

top- [1] P. Billingsley, Convergence of probability measures. John Wiley and Sons, New York (1968) 253. Zbl0172.21201MR233396
- [2] M. Duflo, Méthodes Récursives Aléatoires. Techniques Stochastiques, Masson, Paris (1990) 359. Zbl0703.62084MR1082344
- [3] M. Duflo, Algorithmes Stochastiques. Math. Appl. 23 (1996) 319. Zbl0882.60001MR1612815
- [4] T.E. Harris, The existence of stationnary measures for certain markov processes. Proc. of the 3rd Berkeley Symposium on Mathematical Statistics and Probability 2 (1956) 113–124. Zbl0072.35201
- [5] S.P. Meyn and R.L Tweedie, Markov Chains and Stochastic Stability. Springer-Verlag (1993) 550. Zbl0925.60001MR1287609
- [6] A.G. Pakes, Some conditions for ergodicity and recurrence of markov chains. Oper. Res. 17 (1969) 1048–1061. Zbl0183.46902

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