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A stochastic ordering of partial sums of independent random variables and of some random processes
Published online by Cambridge University Press: 14 July 2016
Abstract
In this paper we first prove an arrangement-decreasing property of partial sums of independent random variables when they are partially ordered through the likelihood ratio ordering. We then apply a similar argument to obtain a stochastic ordering of random processes via a comparison of their parameter functions, with special applications to Poisson and Wiener processes. Finally, in Section 4 we present some applications in reliability theory, queueing, and first-passage problems.
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- Copyright © Applied Probability Trust 1992
Footnotes
Research partially supported by AFOSR under Grant Nos 88–0040 and 89–0221.
Research partially supported by AFOSR under Grant Nos 88–0040 and 89–0221.
Research partially supported by the NSF under Grant No DMS-9001721.
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