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Ergodicity of a certain class of non Feller models : applications to 𝐴𝑅𝐶𝐻 and Markov switching models

Jean-Gabriel Attali (2004)

ESAIM: Probability and Statistics

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.

Ergodicity of a certain class of Non Feller Models: Applications to ARCH and Markov switching models

Jean-Gabriel Attali (2010)

ESAIM: Probability and Statistics

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.

Estimates for simple random walks on fundamental groups of surfaces

Laurent Bartholdi, Serge Cantat, Tullio Ceccherini-Silberstein, Pierre de la Harpe (1997)

Colloquium Mathematicae

Numerical estimates are given for the spectral radius of simple random walks on Cayley graphs. Emphasis is on the case of the fundamental group of a closed surface, for the usual system of generators.

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