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Structural properties of Markov chains with weak and strong interactions

Author

Listed:
  • Zhang, Q.
  • Yin, G.

Abstract

Markov chains have been frequently used to characterize uncertainty in many real-world problems. Quite often, these Markov chains can be decomposed into a vector consisting of fast and slow components; these components are coupled through weak and strong interactions. The main goal of this work is to study the structural properties of such Markov chains. Under mild conditions, it is proved that the underlying Markov chain can be approximated in the weak topology of L2 by an aggregated process. Moreover, the aggregated process is shown to converge in distribution to a Markov chain as the rate of fast transitions tends to infinity. Under an additional Lipschitz condition, error bounds of the approximation sequences are obtained.

Suggested Citation

  • Zhang, Q. & Yin, G., 1997. "Structural properties of Markov chains with weak and strong interactions," Stochastic Processes and their Applications, Elsevier, vol. 70(2), pages 181-197, October.
    • Handle: RePEc:eee:spapps:v:70:y:1997:i:2:p:181-197
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    Cited by:

    1. Feng, Cheng-Min & Wu, Pei-Ju & Chia, Kai-Chieh, 2010. "A hybrid fuzzy integral decision-making model for locating manufacturing centers in China: A case study," European Journal of Operational Research, Elsevier, vol. 200(1), pages 63-73, January.
    2. Parpas, Panos & Webster, Mort, 2014. "A stochastic multiscale model for electricity generation capacity expansion," European Journal of Operational Research, Elsevier, vol. 232(2), pages 359-374.
    3. G. Yin, 2001. "On Limit Results for a Class of Singularly Perturbed Switching Diffusions," Journal of Theoretical Probability, Springer, vol. 14(3), pages 673-697, July.

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