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

Jean-Gabriel Attali

ESAIM: Probability and Statistics (2004)

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

Abstract

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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.

How to cite

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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 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

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  1. [1] P. Billingsley, Convergence of probability measures. John Wiley and Sons, New York (1968) 253. Zbl0172.21201MR233396
  2. [2] M. Duflo, Méthodes Récursives Aléatoires. Techniques Stochastiques, Masson, Paris (1990) 359. Zbl0703.62084MR1082344
  3. [3] M. Duflo, Algorithmes Stochastiques. Math. Appl. 23 (1996) 319. Zbl0882.60001MR1612815
  4. [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. [5] S.P. Meyn and R.L Tweedie, Markov Chains and Stochastic Stability. Springer-Verlag (1993) 550. Zbl0925.60001MR1287609
  6. [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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