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Discrete Probability and Algorithms pp 1–9Cite as

On Simulating a Markov Chain Stationary Distribution when Transition Probabilities are Unknown

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Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 72))

Abstract

We present an algorithm which, given a n-state Markov chain whose steps can be simulated, outputs a random state whose distribution is within ϵ of the stationary distribution, using O(n)space and O(ϵ-2τ) time, where is a certain “average hitting time” parameter of the chain.

Research supported by N.S.F. Grant DMS92-24857.

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References

  1. D.J. Aldous. Reversible Markov chains and random walks on graphs. Book in preparation, 1995.

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  2. S. Asmussen, P.W. Glynn, and H. Thorisson. Stationarity detection in the initial transient problem. A CM Trans. Modeling and Computer Sim., 2: 130–157, 1992

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  3. F.P. Kelly. Stochastic models of computer communication networks. J. Royal Statist. Soc, B 47: 379–395, 1985.

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  4. L.A. McGeoch and D. Sleator. Workshop on On-Line Algorithms. American Math. Soc, Providence, RI, 1992.

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  5. W.J. Stewart. Numerical Solutions of Markov Chains. Marcel Dekker, New York, 1991.

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Author information

Authors and Affiliations

  1. Department of Statistics, University of California, Berkeley, CA, 94720, USA

    David Aldous

Authors
  1. David Aldous
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Editor information

Editors and Affiliations

  1. Department of Statistics, University of California, Berkeley, CA, 94720, USA

    David Aldous

  2. Department of Mathematics, Harvard University, Cambridge, MA, 02138, USA

    Persi Diaconis

  3. Department of Computer Science Courant Institute, New York University, 251 Mercer Street, New York, NY, 10012, USA

    Joel Spencer

  4. Department of Statistics, The Wharton School University of Pennsylvania, 3000 Steinberg Hall-Dietrich Hall, Philadelphia, PA, 19104-6302, USA

    J. Michael Steele

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© 1995 Springer Science+Business Media New York

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Aldous, D. (1995). On Simulating a Markov Chain Stationary Distribution when Transition Probabilities are Unknown. In: Aldous, D., Diaconis, P., Spencer, J., Steele, J.M. (eds) Discrete Probability and Algorithms. The IMA Volumes in Mathematics and its Applications, vol 72. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0801-3_1

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  • DOI: https://doi.org/10.1007/978-1-4612-0801-3_1

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-6905-2

  • Online ISBN: 978-1-4612-0801-3

  • eBook Packages: Springer Book Archive

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