Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-25T04:08:00.861Z Has data issue: false hasContentIssue false
  • English
  • Français

Stabilité de la récurrence nulle pour certaines chaines de Markov perturbées

Published online by Cambridge University Press:  14 July 2016

C. Cocozza-Thivent ,
C. Kipnis  and
M. Roussignol
C. Cocozza-Thivent*
Affiliation:
Université Pierre et Marie Curie
C. Kipnis*
Affiliation:
Université Pierre et Marie Curie
M. Roussignol*
Affiliation:
Université Pierre et Marie Curie
*
∗ Membres du Laboratoire de Probabilités, associé au C.N.R.S. n° 224, Université Pierre et Marie Curie, 4, Place Jussieu, Tour 56, 75230 Paris Cedex 05, France.
∗ Membres du Laboratoire de Probabilités, associé au C.N.R.S. n° 224, Université Pierre et Marie Curie, 4, Place Jussieu, Tour 56, 75230 Paris Cedex 05, France.
∗ Membres du Laboratoire de Probabilités, associé au C.N.R.S. n° 224, Université Pierre et Marie Curie, 4, Place Jussieu, Tour 56, 75230 Paris Cedex 05, France.
Get access Rights & Permissions [Opens in a new window]

Abstract

We investigate how the property of null-recurrence is preserved for Markov chains under a perturbation of the transition probability. After recalling some useful criteria in terms of the one-step transition nucleus we present two methods to determine barrier functions, one in terms of taboo potentials for the unperturbed Markov chain, and the other based on Taylor's formula.

Keywords

PERTURBATION OF MARKOV CHAINSSTABILITY OF NULL-RECURRENCEBARRIER FUNCTION
Type
Research Papers
Information
Journal of Applied Probability , Volume 20 , Issue 3 , September 1983 , pp. 482 - 504
Copyright
Copyright © Applied Probability Trust 1983 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bibliographie

[1] Cocozza-Thivent, C. and Roussignol, M. (1983) Stabilité de la recurrence d'une chaîne de Markov sous l'effet d'une perturbation. Stochastics 9, 125–137.Google Scholar
[2] Filonov, Ju. P. (1979) Recurrence of finite-dimensional Markov chains. Theory Prob. Math. Statist. 17, 147–153.Google Scholar
[3] Filonov, Ju. P. (1980) Stability of the properties of transience and recurrence of Markov chains. Theory Prob. Math. Statist. 19, 155–167.Google Scholar
[4] Mertens, J. F., Samuel-Cahn, E. and Zamir, S. (1978) Necessary and sufficient conditions for recurrence and transience of Markov chains, in terms of inequalities. J. Appl. Prob. 15, 848–851.Google Scholar
[5] Pakes, A. G. (1969) Some conditions of ergodicity and recurrence of Markov chains. Operat. Res. 17, 1058–1061.Google Scholar
[6] Rosberg, Z. (1981) A note on the ergodicity of Markov chains. J. Appl. Prob. 18, 112–121.Google Scholar
[7] Spitzer, F. (1964) Principles of Random Walk. Van Nostrand, Princeton, NJ.Google Scholar
[8] Tweedie, R. L. (1975) The robustness of positive recurrence and recurrence of Markov chains under perturbations of the transition probabilities. J. Appl. Prob. 12, 744–752.Google Scholar
[9] Tweedie, R. L. (1975) Relations between ergodicity and mean drift for Markov chains. Austral. J. Statist. 17, 96–106.CrossRefGoogle Scholar
[10] Tweedie, R. L. (1980) Perturbations of countable Markov chains and processes. Ann. Inst. Statist. Math. 32, 283–290.Google Scholar