Analysis of initial transient deletion for replicated steady-state simulations. (English) Zbl 0752.65100
Let \((X(t): t\geq 0)\) be a real stochastic process. It is assumed the existence of finite constants \(\alpha\) and \(\sigma\) such that \(t^{1/2}({1\over t}\int^ t_ 0X(s)ds-\alpha))\) is \(N(0,\sigma^ 2)\)-distributed for \(t\to\infty\). The method of independent replications with initial transient delection for generating of confidence intervals for \(\alpha\) is considered.
Reviewer: W.Grecksch (Merseburg)
MSC:
| 65C99 | Probabilistic methods, stochastic differential equations |
| 62M09 | Non-Markovian processes: estimation |
| 62F25 | Parametric tolerance and confidence regions |
Keywords:
replicated steady-state simulations; stochastic process; method of independent replications; initial transient delection; generating of confidence intervalsReferences:
| [1] | Chung, K. L., A Course in Probability Theory (1974), Academic Press: Academic Press New York · Zbl 0159.45701 |
| [2] | Doob, J. L., Stochastic Processes (1953), John Wiley: John Wiley New York · Zbl 0053.26802 |
| [3] | Ethier, S. N.; Kurtz, T. G., Markov Processes: Characterization and Convergence (1986), John Wiley: John Wiley New York · Zbl 0592.60049 |
| [4] | Gafarian, A. V.; Ancker, C. J.; Morisaku, T., Evaluation of commonly used rules for detecting ‘steady-state’ in computer simulation, Naval Research Logistics Quarterly, 25, 511-529 (1978) · Zbl 0397.68098 |
| [5] | Glynn, P. W., Limit theorems for the method of replication, Stochastic Models, 4, 344-350 (1987) |
| [6] | Glynn, P. W.; Heidelberger, P., Analysis of initial transient deletion for parallel, steady-state simulations, IBM Research Report RC 15260 (1989), Yorktown Heights, New York, to appear in SIAM J. Sci. Statist. Comput. · Zbl 0756.65164 |
| [7] | Glynn, P. W.; Heidelberger, P., Experiments with initial transient deletion for parallel, replicated steady-state simulations, IBM Research Report RC 15770 (1990), Yorktown Heights, New York, to appear in Management Sci. |
| [8] | Glynn, P. W.; Heidelberger, P., Analysis of parallel, replicated simulations under a completion time constraint, ACM Transactions on Modeling and Computer Simulation, 1, 1, 3-23 (1991) · Zbl 0842.65099 |
| [9] | Glynn, P. W.; Whitt, W., Sufficient conditions for functional-limit-theorem version \(L = λW \), Queueing Systems, Theory and Applications, 1, 279-287 (1987) · Zbl 0681.60097 |
| [10] | Heidelberger, P.; Welch, P. D., Simulation run length control in the presence of an initial transient, Operations Research, 31, 1109-1114 (1983) · Zbl 0532.65097 |
| [11] | Heidelberger, P., Discrete event simulations and parallel processing: statistical properties, SIAM Journal on Scientific and Statistical Computing, 9, 1114-1132 (1988) · Zbl 0661.68115 |
| [12] | Karlin, S.; Taylor, H. M., A First Course in Stochastic Processes (1975), Academic Press: Academic Press New York · Zbl 0315.60016 |
| [13] | Kelton, W. D., The startup problem in discrete event simulation, (Technical Report 80-1 (1980), Department of Industrial Engineering, University of Wisconsin: Department of Industrial Engineering, University of Wisconsin Madison, WI) · Zbl 0371.94051 |
| [14] | Kelton, W. D.; Law, A. M., A new approach for dealing with the startup problem in discrete event simulation, Naval Research Logistics Quarterly, 30, 641-658 (1980) · Zbl 0532.65099 |
| [15] | Newman, C. M.; Wright, A. L., An invariance principle for certain dependent sequences, Annals of Probability, 9, 671-675 (1981) · Zbl 0465.60009 |
| [16] | Nummelin, E.; Tuominen, P., Geometric ergodicity of Harris recurrent Markov chains with applications to renewal theory, Stochastic Processes and Their Applications, 12, 187-202 (1982) · Zbl 0484.60056 |
| [17] | Pitman, J., Uniform rates of convergence for Markov chain transition probabilities, Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, 29, 193-227 (1974) · Zbl 0373.60077 |
| [18] | Schmeiser, B. W., Batch size effects in the analysis of simulation output, Operations Research, 30, 556-568 (1982) · Zbl 0484.65087 |
| [19] | Schruben, L. W., Control of initialization bias in multi-variate simulation response, Communications of the ACM, 24, 246-252 (1981) |
| [20] | Schruben, L. W., Detecting initialization bias in simulation output, Operations Research, 30, 569-590 (1982) · Zbl 0484.65043 |
| [21] | Schruben, L. W.; Singh, H.; Tierney, L., Optimal tests for initialization bias in simulation output, Operations Research, 31, 1167-1178 (1983) · Zbl 0538.62075 |
| [22] | Smith, W. L., Regenerative stochastic processes, (Proceedings of the Royal Society of London Series A, 232 (1955)), 6-31 · Zbl 0067.36301 |
| [23] | Wilson, J. R.; Pritsker, A. A.B., A survey of research on the simulation start-up problem, Simulation, 31, 55-58 (1978) |
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