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 
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     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},
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     year = {2004},
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     url = {http://www.numdam.org/articles/10.1051/ps:2004003/}
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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://www.numdam.org/articles/10.1051/ps:2004003/

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