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|a (JST)3689124
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|a DE-627
|b ger
|c DE-627
|e rakwb
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|a eng
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|a 60K25
|2 MSC
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|a Harrison, J. Michael
|e verfasserin
|4 aut
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|a Some Stochastic Bounds for Dams and Queues
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|c 1977
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|a Text
|b txt
|2 rdacontent
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|a Computermedien
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|2 rdamedia
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|a Online-Ressource
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|a Let X = {X(t), t ≥ 0} be a process of the form X(t) = Z(t) - ct, where c is a positive constant and Z is an infinitely divisible, nondecreasing pure jump process. Assuming E[X(t)] < 0, let U be the d.f. of M = sup X(t). As is well known, U is the contents distribution of a dam with input Z and release rate c. If Z is compound Poisson, one can alternately view U as the waiting time distribution for an M/G/1 queue or 1 - U as the ruin function for a risk process. Letting X and X<sub>0</sub> be two processes of the indicated form, it is shown that U ≤ U<sub>0</sub> if the two jump measures are ordered in a sense weaker than stochastic dominance. In the case where E(M) = <tex-math>$E(M_{0})$</tex-math>, a different condition on the jump measures yields E[f(M)] ≤ <tex-math>$E[f(M_{0})]$</tex-math> for all concave f, this resulting from second-order stochastic dominance of the supremum distributions. By way of application, processes with deterministic jumps are shown to be extremal in certain ways, and those with exponential jumps are shown to be extremal among the class having IFR jump distribution. Finally, an extremal property of Brownian Motion (which is not among the class of processes considered) is demonstrated, this yielding simple bounds for E[f(M)] with f concave or convex. It is shown how all the bounds obtained for U or E[f(M)] can be further sharpened with additional computation.
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|a Copyright 1977 The Institute of Management Sciences
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|a Brownian motion
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|a Collective risk theory
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|a Dam
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|a Infinitely divisible process
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|a M/G/1 queue
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|a Maxima
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|a Second-order stochastic dominance
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|a Stochastic dominance
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|a Storage process
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|a Mathematics
|x Mathematical procedures
|x Approximation
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|a Physical sciences
|x Physics
|x Mechanics
|x Fluid mechanics
|x Brownian motion
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|a Mathematics
|x Pure mathematics
|x Probability theory
|x Random variables
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|a Applied sciences
|x Engineering
|x Transportation
|x Traffic
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|a Philosophy
|x Metaphysics
|x Etiology
|x Determinism
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|a Economics
|x Economic disciplines
|x Financial economics
|x Insurance
|x Insurance expenses
|x Insurance premiums
|x Risk premiums
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|a Mathematics
|x Pure mathematics
|x Probability theory
|x Random variables
|x Stochastic processes
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|a Mathematics
|x Pure mathematics
|x Probability theory
|x Random variables
|x Stochastic processes
|x Poisson process
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|a Mathematics
|x Applied mathematics
|x Statistics
|x Applied statistics
|x Descriptive statistics
|x Statistical distributions
|x Distribution functions
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|a Mathematics
|x Applied mathematics
|x Statistics
|x Applied statistics
|x Descriptive statistics
|x Measures of variability
|x Statistical variance
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|a research-article
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|i Enthalten in
|t Mathematics of Operations Research
|d Institute for Operations Research and the Management Sciences
|g 2(1977), 1, Seite 54-63
|w (DE-627)320435318
|w (DE-600)2004273-5
|x 15265471
|7 nnns
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|g volume:2
|g year:1977
|g number:1
|g pages:54-63
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|u https://www.jstor.org/stable/3689124
|3 Volltext
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|d 2
|j 1977
|e 1
|h 54-63
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