On the classification of Markov chains via occupation measures

Onésimo Hernández-Lerma; Jean Lasserre

Applicationes Mathematicae (2000)

  • Volume: 27, Issue: 4, page 489-498
  • ISSN: 1233-7234

Abstract

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We consider a Markov chain on a locally compact separable metric space X and with a unique invariant probability. We show that such a chain can be classified into two categories according to the type of convergence of the expected occupation measures. Several properties in each category are investigated.

How to cite

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Hernández-Lerma, Onésimo, and Lasserre, Jean. "On the classification of Markov chains via occupation measures." Applicationes Mathematicae 27.4 (2000): 489-498. <http://eudml.org/doc/219291>.

@article{Hernández2000,
abstract = {We consider a Markov chain on a locally compact separable metric space $X$ and with a unique invariant probability. We show that such a chain can be classified into two categories according to the type of convergence of the expected occupation measures. Several properties in each category are investigated.},
author = {Hernández-Lerma, Onésimo, Lasserre, Jean},
journal = {Applicationes Mathematicae},
keywords = {absolute continuity; positive Harris recurrence; setwise convergence; measures; type of convergence; expected occupation measures},
language = {eng},
number = {4},
pages = {489-498},
title = {On the classification of Markov chains via occupation measures},
url = {http://eudml.org/doc/219291},
volume = {27},
year = {2000},
}

TY - JOUR
AU - Hernández-Lerma, Onésimo
AU - Lasserre, Jean
TI - On the classification of Markov chains via occupation measures
JO - Applicationes Mathematicae
PY - 2000
VL - 27
IS - 4
SP - 489
EP - 498
AB - We consider a Markov chain on a locally compact separable metric space $X$ and with a unique invariant probability. We show that such a chain can be classified into two categories according to the type of convergence of the expected occupation measures. Several properties in each category are investigated.
LA - eng
KW - absolute continuity; positive Harris recurrence; setwise convergence; measures; type of convergence; expected occupation measures
UR - http://eudml.org/doc/219291
ER -

References

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  1. [1] J. L. Doob, Measure Theory, Grad. Texts in Math. 143, Springer, New York, 1994. 
  2. [2] S. R. Foguel, The Ergodic Theory of Markov Processes, Van Nostrand Math. Stud. 21, Van Nostrand, London, 1969. 
  3. [3] O. Hernández-Lerma and J. B. Lasserre, Ergodic theorems and ergodic decompostion for Markov chains, Acta Appl. Math. 54 (1998), 99-119. Zbl1002.60559
  4. [4] O. Hernández-Lerma and J. B. Lasserre, Further criteria for positive Harris recurrence of Markov chains, Proc. Amer. Math. Soc., to appear. Zbl0970.60078
  5. [5] S. Horowitz, Transition probabilities and contractions of L ∞ , Z. Wahrsch. Verw. Gebiete 24 (1972), 263-274. Zbl0228.60028
  6. [5] A. Lasota and M. C. Mackey, Chaos, Fractals and Noise: Stochastic Aspects of Dynamics, Appl. Math. Sci. 97, Springer, New York, 1994. Zbl0784.58005
  7. [7] S. P. Meyn and R. L. Tweedie, Markov Chains and Stochastic Stability, Springer, London, 1993. Zbl0925.60001
  8. [8] J. Neveu, Sur l'irréductibilité des chaînes de Markov, Ann. Inst. H. Poincaré 8 (1972), 249-254. Zbl0241.60049
  9. [9] T. V. Panchapagesan, Baire and σ -Borel characterizations of weakly compact sets in M ( T ) , Trans. Amer. Math. Soc. 350 (1999), 4839-4847. 
  10. [10] H. L. Royden, Real Analysis, 3rd ed., Macmillan, New York, 1988. Zbl0704.26006
  11. [11] K. Yosida, Functional Analysis, 6th ed., Grundlehren Math. Wiss. 123, Springer, Berlin, 1980. Zbl0435.46002

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