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

Jean-Gabriel Attali

ESAIM: Probability and Statistics (2010)

  • 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 ARCH and Markov switching models." ESAIM: Probability and Statistics 8 (2010): 76-86. <http://eudml.org/doc/104324>.

@article{Attali2010,
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.; invariant measure; ARCH models; Markov switching},
language = {eng},
month = {3},
pages = {76-86},
publisher = {EDP Sciences},
title = {Ergodicity of a certain class of Non Feller Models: Applications to ARCH and Markov switching models},
url = {http://eudml.org/doc/104324},
volume = {8},
year = {2010},
}

TY - JOUR
AU - Attali, Jean-Gabriel
TI - Ergodicity of a certain class of Non Feller Models: Applications to ARCH and Markov switching models
JO - ESAIM: Probability and Statistics
DA - 2010/3//
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.; invariant measure; ARCH models; Markov switching
UR - http://eudml.org/doc/104324
ER -

References

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  1. P. Billingsley, Convergence of probability measures. John Wiley and Sons, New York (1968) 253.  Zbl0172.21201
  2. M. Duflo, Méthodes Récursives Aléatoires. Techniques Stochastiques, Masson, Paris (1990) 359.  Zbl0703.62084
  3. M. Duflo, Algorithmes Stochastiques. Math. Appl.23 (1996) 319.  
  4. T.E. Harris, The existence of stationnary measures for certain markov processes. Proc. of the 3rd Berkeley Symposium on Mathematical Statistics and Probability2 (1956) 113–124.  
  5. S.P. Meyn and R.L Tweedie, Markov Chains and Stochastic Stability. Springer-Verlag (1993) 550.  Zbl0925.60001
  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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