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Monte Carlo simulation of the renewal function

Published online by Cambridge University Press:  14 July 2016

Mark Brown ,
Herbert Solomon  and
Michael A. Stephens
Mark Brown
Affiliation:
Florida State University
Herbert Solomon
Affiliation:
Stanford University
Michael A. Stephens*
Affiliation:
Simon Fraser University
*
∗∗∗Postal address: Department of Mathematics, Simon Fraser University, Burnaby, B.C., Canada V5A 1S6.
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Abstract

The problem of Monte Carlo estimation of M(t) = EN(t), the expected number of renewals in [0, t] for a renewal process with known interarrival time distribution F, is considered. Several unbiased estimators which compete favorably with the naive estimator, N(t), are presented and studied. An approach to reduce the variance of the Monte Carlo estimator is developed and illustrated.

Keywords

MONTE CARLO SIMULATION IN ESTIMATIONVARIANCE REDUCTIONRENEWAL THEORYCUMULATIVE PROCESSES
Type
Research Papers
Information
Journal of Applied Probability , Volume 18 , Issue 2 , June 1981 , pp. 426 - 434
Copyright
Copyright © Applied Probability Trust 

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Footnotes

∗

Now at City College, CUNY. Postal address: 67 Tintern Lane, Scarsdale, NY 10583, U.S.A.

Research partially supported under U.S. Army Research Office Grant DAAG–29–77–G–0031 and Office of Naval Research Contract No. N00014–76–C–0475(NR–042–257) at Stanford University.

References

[1] Brown, M. and Ross, S. M. (1972) Asymptotic properties of cumulative processes. SIAM J. Appl. Math. 22, 93–105.Google Scholar
[2] Feller, W. (1970) An Introduction to Probability Theory and Its Applications, Vol. II, 2nd edn. Wiley, New York.Google Scholar
[3] Smith, W. L. (1955) Regenerative stochastic processes. Proc. R. Soc. London A 232, 6–31.Google Scholar