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Une condition suffisante de recurrence pour des chaines de Markov sur la droite

Part of the Lecture Notes in Mathematics book series (LNM,volume 1064)

Abstract

A direct, elementary, proof is given to the following result: "Let P(x,dy) a transition probability on the real line. Assume that:

  1. i)

    for f continuous and bounded, Pf is continuous.

  2. ii)

    P is irreductible, with respect to open sets.

  3. iii)

    for some constant K, P(x, ]−∞, −K[)=O for x close enough to +∞ and P(x, ]+K, +∞[)=O for x close enough to −∞.

  4. iv)

    for x outside a compact set, ∫y P(x,dy)=x

Then the Markov chain associated to P is topologically recurrent on the line" A similar result is given on ℤ.

Keywords

  • Chaine Associee
  • Question Suivante
  • Proposition Suivante
  • Voisinage Versus
  • Etant Centree

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. C. Cocozza-Thivent, C. Kipnis, M. Roussignol (1982) Stabilité de la récurrence nulle pour certaines chaînes de Markov perturbées. (à paraître)

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  2. S.R. Foguel (1973). The ergodic theory of positive operators on continuous functions. Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Vol XXVII Fasc. 1, 19–51

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  3. A. Friedman (1975) Stochastic differential equations and applications. Academic Press.

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  4. J. Neveu (1972). Martingales à temps discret. Masson et Cie

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  5. D. Revuz (1975). Markov chains. North Holland pub.

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© 1984 Springer-Verlag

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Derriennic, Y. (1984). Une condition suffisante de recurrence pour des chaines de Markov sur la droite. In: Heyer, H. (eds) Probability Measures on Groups VII. Lecture Notes in Mathematics, vol 1064. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0073633

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  • DOI: https://doi.org/10.1007/BFb0073633

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13341-4

  • Online ISBN: 978-3-540-38874-6

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