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: 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, Volume 8 (2004), pp. 76-86. doi : 10.1051/ps:2004003. http://archive.numdam.org/articles/10.1051/ps:2004003/

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