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Simulation Output Analysis for General State Space Markov Chains

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Applied Probability-Computer Science: The Interface Volume 1

Part of the book series: Progress in Computer Science ((PCS,volume 2))

Abstract

The statistical analysis of simulation output has been the primary focus of recent research in simulation methodology. Methods have been developed which permit the simulator to construct confidence intervals for steady-state characteristics of the system being simulated. The principal methods in current use are autoregressive modeling, batch means, regenerative, and replication. With the exception of the replication method, all methods are bas d on just one simulation run. These methods for constructing confidence intervals are all based on central limit theorems for the underlying stochastic processes being simulated. Thus all methods are only valid asymptotically for long simulation runs.

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References

  1. Akaike, H. (1976). Canonical Correlation Analysis of Time Series and the use of an Information Criterion. Systerns Identification: Advances and Case Studies, R. K. Mehra and D. G. Lainioties, eds., Academic Press, New York.

    Google Scholar 

  2. Akaike, H. and G. Kitigawa (1978). A Procedure for the Modeling of Non-stationary Time Series. Ann. Inst. Statist. Math., 30, B, 351–353.

    Google Scholar 

  3. Athreya, K. B. and P. Ney (1978). A New Approach to the Limit Theory of Markov Chains. Trans. Amer. Math. Soc., 245. 493–501.

    Google Scholar 

  4. Billingsley, P. 1968 ). Convergence of Probability Measures. John Wiley, New York.

    Google Scholar 

  5. Crane, M. A. and D. L. Iglehart (1975). Simulating Stable Stochastic Systems, IV: Approximation Techniques. Management Sci., 21, 1215–1224.

    Google Scholar 

  6. Doob, J. L. (1953). Stochastic Processes. John Wiley and Sons, New York.

    Google Scholar 

  7. Fossett, L. D. (1979). Simulating Generalized Semi-Markov Processes. Ph.D. Dissertation, Department of Operations Research, Stanford University.

    Google Scholar 

  8. Glynn, P. W. (1980). An Approach to Regenerative Simulation on a General State Space. Technical Report 53, Department of Operations Research, Stanford University.

    Google Scholar 

  9. Glynn, P. W. (1981). Forthcoming Technical Report, Department of Operations Research, Stanford University.

    Google Scholar 

  10. Harris, T. E. (1956). The Existence of Stationary Measures for Certain Markov Processes. Proc. Third Berkeley Symposium on Mathematical Statistics and Probability, Vol. 2, Jersey Neyman, ed., University of California Press, Berkeley.

    Google Scholar 

  11. Hordijk, A. and R. Schassberger (1982). Weak Convergence for Generalized Semi-Markov Processes. To appear in Stochastic Process. Appl.

    Google Scholar 

  12. Jow, L. (1981). Forthcoming Technical Report. Department of Operations Research, Stanford University.

    Google Scholar 

  13. Nummelin, E. (1978). A Splitting Technique for Harris Recurrent Markov Chains. Z. Wahrsch. Verw. Gebiete., 43, 309–318.

    Google Scholar 

  14. Orey, S. (1959). Recurrent Markov Chains. Pacific J. Math., 9, 805–827.

    Google Scholar 

  15. Smith, W. L. (1955). Regenerative Stochastic Processes. Proc. Soc. London, Ser. A, 232, 6–31.

    Google Scholar 

  16. Whitt, W. (1980). Continuity of Generalized Semi-Markov Processes. Math. Oper. Res.,. 5, 494–501.

    Google Scholar 

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© 1982 Birkhäuser Boston, Inc.

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Glynn, P.W., Iglehart, D.L. (1982). Simulation Output Analysis for General State Space Markov Chains. In: Disney, R.L., Ott, T.J. (eds) Applied Probability-Computer Science: The Interface Volume 1. Progress in Computer Science, vol 2. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-5791-2_3

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  • DOI: https://doi.org/10.1007/978-1-4612-5791-2_3

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-1-4612-5793-6

  • Online ISBN: 978-1-4612-5791-2

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