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Ergodicity in Parametric Nonstationary Markov Chains: An Application to Simulated Annealing Methods

Author

Listed:
  • Shoshana Anily

    (University of British Columbia, Vancouver, British Columbia)

  • Awi Federgruen

    (Columbia University, New York, New York)

Abstract

A nonstationary Markov chain is weakly ergodic if the dependence of the state distribution on the starting state vanishes as time tends to infinity. A chain is strongly ergodic if it is weakly ergodic and converges in distribution. In this paper we show that the two ergodicity concepts are equivalent for finite chains under rather general (and widely verifiable) conditions. We discuss applications to probabilistic analyses of general search methods for combinatorial optimization problems (simulated annealing).

Suggested Citation

  • Shoshana Anily & Awi Federgruen, 1987. "Ergodicity in Parametric Nonstationary Markov Chains: An Application to Simulated Annealing Methods," Operations Research, INFORMS, vol. 35(6), pages 867-874, December.
    • Handle: RePEc:inm:oropre:v:35:y:1987:i:6:p:867-874
    DOI: 10.1287/opre.35.6.867
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    Cited by:

    1. Tapas Mishra & Claude Diebolt & Mamata Parhi, 2010. "Stochasticity in Population and Economic Growth with Past Dependence," Working Papers 10-10, Association Française de Cliométrie (AFC).
    2. Andreas Nolte & Rainer Schrader, 2000. "A Note on the Finite Time Behavior of Simulated Annealing," Mathematics of Operations Research, INFORMS, vol. 25(3), pages 476-484, August.

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