Ergodicity of a certain class of non Feller models : applications to 𝐴𝑅𝐶𝐻 and Markov switching models
ESAIM: Probability and Statistics, Tome 8 (2004), pp. 76-86.

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.

DOI : 10.1051/ps:2004003
Classification : 60B05, 60B10, 60J10
Mots clés : ergodic, Markov chain, Feller, quasi-Feller, invariant measure, geometric ergodicity, rate of convergence, $ARCH$ models, Markov switching
@article{PS_2004__8__76_0,
     author = {Attali, Jean-Gabriel},
     title = {Ergodicity of a certain class of non {Feller} models : applications to $\textit {ARCH}$ and {Markov} switching models},
     journal = {ESAIM: Probability and Statistics},
     pages = {76--86},
     publisher = {EDP-Sciences},
     volume = {8},
     year = {2004},
     doi = {10.1051/ps:2004003},
     mrnumber = {2085607},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1051/ps:2004003/}
}
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
SP  - 76
EP  - 86
VL  - 8
PB  - EDP-Sciences
UR  - http://archive.numdam.org/articles/10.1051/ps:2004003/
DO  - 10.1051/ps:2004003
LA  - en
ID  - PS_2004__8__76_0
ER  - 
%0 Journal Article
%A Attali, Jean-Gabriel
%T Ergodicity of a certain class of non Feller models : applications to $\textit {ARCH}$ and Markov switching models
%J ESAIM: Probability and Statistics
%D 2004
%P 76-86
%V 8
%I EDP-Sciences
%U http://archive.numdam.org/articles/10.1051/ps:2004003/
%R 10.1051/ps:2004003
%G en
%F PS_2004__8__76_0
Attali, Jean-Gabriel. Ergodicity of a certain class of non Feller models : applications to $\textit {ARCH}$ and Markov switching models. ESAIM: Probability and Statistics, Tome 8 (2004), pp. 76-86. doi : 10.1051/ps:2004003. http://archive.numdam.org/articles/10.1051/ps:2004003/

[1] P. Billingsley, Convergence of probability measures. John Wiley and Sons, New York (1968) 253. | MR | Zbl

[2] M. Duflo, Méthodes Récursives Aléatoires. Techniques Stochastiques, Masson, Paris (1990) 359. | MR | Zbl

[3] M. Duflo, Algorithmes Stochastiques. Math. Appl. 23 (1996) 319. | MR | Zbl

[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. | Zbl

[5] S.P. Meyn and R.L Tweedie, Markov Chains and Stochastic Stability. Springer-Verlag (1993) 550. | MR | Zbl

[6] A.G. Pakes, Some conditions for ergodicity and recurrence of markov chains. Oper. Res. 17 (1969) 1048-1061. | Zbl

Cité par Sources :