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Drift conditions and invariant measures for Markov chains

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  • Tweedie, R. L.
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    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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    Bibliographic Info

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 92 (2001)
    Issue (Month): 2 (April)
    Pages: 345-354

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    Handle: RePEc:eee:spapps:v:92:y:2001:i:2:p:345-354

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    Related research

    Keywords: Invariant measures Stationary measures Foster-Lyapunov criteria Irreducibility Positive recurrence Ergodicity Drift conditions Harris sets Doeblin decompositions;

    References

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    1. 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.
    2. 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.
    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. 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.
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    Cited by:
    1. 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.
    2. 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.
    3. Frank H. Page & Myrna H. Wooders, 2009. "Endogenous Network Dynamics," Working Papers 2009.28, Fondazione Eni Enrico Mattei.

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