Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-18T04:16:48.504Z Has data issue: false hasContentIssue false
  • English
  • Français

Replication Schemes For Limiting Expectations

Published online by Cambridge University Press:  27 July 2009

Bennett L. Fox  and
Peter W. Glynn
Bennett L. Fox
Affiliation:
Department of MathematicsUniversity of Colorado Denver, Colorado 80204
Peter W. Glynn
Affiliation:
Department of Operations ResearchStanford University Stanford, California 94305-4022
Get access Rights & Permissions [Opens in a new window]

Abstract

We show that natural estimators occurring in certain simulation settings have convergence rates less than the canonical rate usually associated with simulation. These natural estimators use replication schemes that attenuate bias. For some important examples, we find alternative estimators that converge at the canonical rate. The implications of these asymptotic comparisons for choosing good strategies when the computer-time budget is modest are discussed.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 3 , Issue 3 , July 1989 , pp. 299 - 318
Copyright
Copyright © Cambridge University Press 1989

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bratley, P., Fox, B.L., & Schrage, L.E. (1987). A guide to simulation, 2nd Ed.New York: Springer-Verlag.CrossRefGoogle Scholar
Chung, K.L. (1974). A course in probability theory. New York: Academic Press.Google Scholar
Cinlar, E. (1975). Introduction to stochastic processes. Englewood Cliffs, New Jersey: Prentice-Hall.Google Scholar
Fox, B.L. (1988). Numerical methods for transient Markov chains. Technical Report, Cornell University.Google Scholar
Fox, B.L. & Glynn, P.W. (1989). Simulating discounted processes. Management Science, to appear.Google Scholar
Fox, B.L. & Glynn, P.W. (1988). Discrete-time conversion for finite-horizon Markov processes. Technical Report, Cornell University.Google Scholar
Fox, B.L. & Glynn, P.W. (1988). Computing Poisson probabilities. Communications of the ACM 31: 440–445.CrossRefGoogle Scholar
Frolov, A.S. & Chentsov, N.N. (1963). On the calculation of definite integrals dependent on a parameter by the Monte Carlo method. USSR Computational Mathematics and Mathematical Physics 4: 802–807.CrossRefGoogle Scholar
Glynn, P.W. (1986). Monte Carlo optimization of stochastic systems. Proceedings Winter Simulation Conference, Washington, D.C.Google Scholar
Glynn, P.W. (1986). Low-bias steady-state estimation for equilibrium processes. Technical Report, University of Wisconsin.Google Scholar
Glynn, P.W. (1987). Upper bounds on Poisson tail probabilities. Operations Research Letters 6: 9–14.CrossRefGoogle Scholar
Glynn, P.W. (1987). Limit theorems for the method of replication. Stochastic Models 3: 343–350.Google Scholar
Glynn, P.W. (1989). Gradient estimation with common random numbers. Technical Report in preparation.Google Scholar
Glynn, P.W. (1985). Randomized estimators and time integrals. Technical Report, Mathematics Research Center, University of Wisconsin–Madison.Google Scholar
Glynn, P.W. & Whitt, W. (1986). The efficiency of simulation estimators. Technical Report. AT&T Bell Laboratories, Holmdel, New Jersey.Google Scholar
Gross, D., Miller, D.R., & Plastiras, C.G. (1984). Simulation methodologies for transient Markov processes: A comparative study based on multi-echelon reparable item inventory systems. Proceedings Summer Simulation Conference, Boston, Massachusetts.Google Scholar
Heidelberger, P., Cao, X.R., Zazanis, M.A., & Suri, R. (1988). Convergence properties of infinitesimal perturbation analysis estimates. Management Science 34: 1281–1302.Google Scholar
Johnson, L.W. & Riess, R.D. (1982). Numerical analysis. Reading, Massachusetts: Addison-Wesley.Google Scholar
Zazanis, M.A. & Suri, R. (1986). Comparison of perturbation analysis with conventional sensitivity estimates for stochastic systems. Technical Report, University of Wisconsin.Google Scholar