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Drift conditions and invariant measures for Markov chains

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  • Tweedie, R. L.

Abstract

We consider the classical Foster-Lyapunov condition for the existence of an invariant measure for a Markov chain when there are no continuity or irreducibility assumptions. Provided a weak uniform countable additivity condition is satisfied, we show that there are a finite number of orthogonal invariant measures under the usual drift criterion, and give conditions under which the invariant measure is unique. The structure of these invariant measures is also identified. These conditions are of particular value for a large class of non-linear time series models.

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  • Tweedie, R. L., 2001. "Drift conditions and invariant measures for Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 92(2), pages 345-354, April.
    • Handle: RePEc:eee:spapps:v:92:y:2001:i:2:p:345-354
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    References listed on IDEAS

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    1. Cline, Daren B. H. & Pu, Huay-min H., 1999. "Stability of nonlinear AR(1) time series with delay," Stochastic Processes and their Applications, Elsevier, vol. 82(2), pages 307-333, August.
    2. Cline, Daren B. H. & Pu, Huay-min H., 1998. "Verifying irreducibility and continuity of a nonlinear time series," Statistics & Probability Letters, Elsevier, vol. 40(2), pages 139-148, September.
    3. Costa, O. L. V. & Dufour, F., 2000. "Invariant probability measures for a class of Feller Markov chains," Statistics & Probability Letters, Elsevier, vol. 50(1), pages 13-21, October.
    4. Tweedie, Richard L., 1975. "Sufficient conditions for ergodicity and recurrence of Markov chains on a general state space," Stochastic Processes and their Applications, Elsevier, vol. 3(4), pages 385-403, October.
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    Cited by:

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    3. Lee, O. & Shin, D.W., 2008. "Geometric ergodicity and [beta]-mixing property for a multivariate CARR model," Economics Letters, Elsevier, vol. 100(1), pages 111-114, July.
    4. Costa, O.L.V. & Dufour, F., 2005. "On the ergodic decomposition for a class of Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 115(3), pages 401-415, March.
    5. Fu, Jing & Page, Frank & Zigrand, Jean-Pierre, 2022. "Layered networks, equilibrium dynamics, and stable coalitions," LSE Research Online Documents on Economics 118874, London School of Economics and Political Science, LSE Library.
    6. Gong, Rui & Page, Frank & Wooders, Myrna, 2015. "Endogenous correlated network dynamics," LSE Research Online Documents on Economics 65098, London School of Economics and Political Science, LSE Library.
    7. Jing Fu & Frank Page & Jean-Pierre Zigrand, 2023. "Correction to: Layered Networks, Equilibrium Dynamics, and Stable Coalitions," Dynamic Games and Applications, Springer, vol. 13(2), pages 669-704, June.
    8. Jing Fu & Frank Page & Jean-Pierre Zigrand, 2023. "Layered Networks, Equilibrium Dynamics, and Stable Coalitions," Dynamic Games and Applications, Springer, vol. 13(2), pages 636-668, June.

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