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Chebyshev-like inequalities for dam models

Published online by Cambridge University Press:  14 July 2016

Bruce W. Turnbull
Bruce W. Turnbull*
Affiliation:
Cornell University
*
* Now at Stanford University.
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Abstract

A dam model is proposed for which it is assumed that the conditional distributions of the inputs, given the past, are known only to lie in some class M . For selected M , bounds are derived on various quantities of interest such as the mean time to first emptiness. The case of normal inputs is treated in greater detail and a release rule is discussed. The techniques used are similar to those used in the theory of gambling as developed by Dubins and Savage (1965).

Keywords

DAM MODELTHEORY OF GAMBLINGCHEBYSHEV INEQUALITYRELEASE RULENON-MARKOVIAN INPUTS

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 9 , Issue 3 , June 1972, pp. 617 - 629
Copyright
Copyright © Applied Probability Trust 1972 

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Footnotes

This work forms part of the author's doctoral dissertation submitted in the Department of Operations Research, Cornell University. Research supported in part by the National Science Foundation under Grant GK–21460 and by the U.S. Army Research Office under Grant DA–31–124–ARO–D–474.

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