On the classification of Markov chains via occupation measures

• Autorzy: Onésimo Hernández-Lerma , Jean B. Lasserre
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

absolute continuity; positive Harris recurrence; setwise convergence; measures

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2000
• Tom: 27
• Numer: 4
• Strony: 489-498

Daty

wydano

2000

otrzymano

2000-03-23

Twórcy

autor

Onésimo Hernández-Lerma

• Departamento de Matemáticas, CINVESTAV-IPN, Apdo. Postal 14-740, México, D.F. 07000, Mexico

autor

Jean B. Lasserre

• LAAS-CNRS, 7 Avenue du Colonel Roche, 31077 Toulouse Cedex, France

Bibliografia

• [1] J. L. Doob, Measure Theory, Grad. Texts in Math. 143, Springer, New York, 1994.
• [2] S. R. Foguel, The Ergodic Theory of Markov Processes, Van Nostrand Math. Stud. 21, Van Nostrand, London, 1969.
• [3] O. Hernández-Lerma and J. B. Lasserre, Ergodic theorems and ergodic decompostion for Markov chains, Acta Appl. Math. 54 (1998), 99-119.
• [4] O. Hernández-Lerma and J. B. Lasserre, Further criteria for positive Harris recurrence of Markov chains, Proc. Amer. Math. Soc., to appear.
• [5] S. Horowitz, Transition probabilities and contractions of $L_∞$, Z. Wahrsch. Verw. Gebiete 24 (1972), 263-274.
• [5] A. Lasota and M. C. Mackey, Chaos, Fractals and Noise: Stochastic Aspects of Dynamics, Appl. Math. Sci. 97, Springer, New York, 1994.
• [7] S. P. Meyn and R. L. Tweedie, Markov Chains and Stochastic Stability, Springer, London, 1993.
• [8] J. Neveu, Sur l'irréductibilité des chaînes de Markov, Ann. Inst. H. Poincaré 8 (1972), 249-254.
• [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] H. L. Royden, Real Analysis, 3rd ed., Macmillan, New York, 1988.
• [11] K. Yosida, Functional Analysis, 6th ed., Grundlehren Math. Wiss. 123, Springer, Berlin, 1980.