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Recursive moment formulas for regenerative simulation

  • Peter W. Glynn
  • Donald L. Iglehart

Abstract

Let f be a real-valued function defined on the state space of a regenerative process \( \mathop X\limits_ \eqsim = \left\{ {X\left( t \right):t \geqslant 0} \right\}\) with regeneration times 0 = T0 < T1 <..., and suppose that
$$ {r_t} = \frac{1}{t}\int_0^t {f\left( {X\left( s \right)} \right)ds \to r\quad a.s.} $$
(1.1)
as t → ∞.

Keywords

Regenerative Simulation Discrete Time Markov Chain Confidence Inter Strong Markov Property Absolute Summability 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. M.A. Crane, D.L. Iglehart (1975). “Stimulating Stable Stochastic Systems, III: Regenerative Processes and Discrete-Event Stimulations”, Oper. Res. 23, 33–45.MathSciNetzbMATHCrossRefGoogle Scholar
  2. P.W. Glynn (1982), “Asymptotic Theory for Nonparametric Confidence Intervals”, Technical Report no 19 Dept. of Operations Research, Stanford University, Stanford, CA.Google Scholar
  3. P.W. Glynn and D.L. Iglehart (1984), “The Joint Limit Distribution of Sample Mean and the Regenerative Variance Estimator”. Forthcoming technical report, Dept. of Operations Research, Stanford University, Stanford, CA.Google Scholar
  4. A. Hordijk, D.L. Iglehart and R. Schassberger (1976). “Discrete-Time Methods of Stimulating Continuous-Time Markov Chains”, Advances in Appl. Probability 8, 772–788.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1986

Authors and Affiliations

  • Peter W. Glynn
    • 1
  • Donald L. Iglehart
    • 1
    • 2
  1. 1.University of WisconsinUSA
  2. 2.Stanford UniversityUSA

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