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1.
For every integrable allocation (X
1,X
2, ...,X
n
) of a random endowmentY=
i
=1/n
X
i
amongn agents, there is another allocation (X
1*,X
2*, ...,X
n
*) such that for every 1in,X
i
* is a nondecreasing function ofY (or, (X
1*,X
2*, ...,X
n
*) areco-monotone) andX
i
* dominatesX
i
by Second Degree Dominance.If (X
1*,X
2*, ...,X
n
*) is a co-monotone allocation ofY=
i
=1/n
X
i
*, then for every 1in, Y is more dispersed thanX
i
* in the sense of the Bickel and Lehmann stochastic order.To illustrate the potential use of this concept in economics, consider insurance markets. It follows that unless the uninsured position is Bickel and Lehmann more dispersed than the insured position, the existing contract can be improved so as to raise the expected utility of both parties, regardless of their (concave) utility functions. 相似文献
2.
A general stream of n types of customers arrives at a Single Server station where service is non-preemptive, the server may undergo Poisson breakdowns and insertion of idle times is allowed. If ξ(k) and c(k) are, respectively, the expected service time and sojourn cost per unit time of a type k customer (1?k?n), call k “V.I.P.” type if ξ(k)/c(k) = min1?i?n[ξ(i)/sbc(i)].We show that any right-of-way service policy can be improved by a policy that grants V.I.P. customers priority over all others, and never inserts idle time when a V.I.P. customer is present.We further show that if the arrival stream is Poisson, the so-called “cμ” priority rule (applied with no delays) is optimal in the class of all service policies, and not just among those of a priority nature. 相似文献
3.
A single server facility is equipped to perform a collection of operations. The service rendered to a customer is a branching process of operations. While the performance of an operation may not be interrupted before its completion, once completed, the required follow-up work may be delayed, at a cost per unit time of waiting that depends on the type and load of work being delayed. Under some probabilistic assumptions on the nature of the required service and on the stream of customers, the problem is to find service schedules that minimize expected costs. The authors generalize results of Bruno [2], Chazan, Konheim and B. Weiss [4], Harrison [8], Klimov [10], Konheim [11], and Meilijson and G. Weiss [13], using a dynamic programming approach. 相似文献
4.
Isaac Meilijson 《Israel Journal of Mathematics》1990,72(3):341-352
This paper presents formulas and asymptotic expansions for the expected number of vertices and the expected volume of the
convex hull of a sample ofn points taken from the uniform distribution on ad-dimensional ball. It is shown that the expected number of vertices is asymptotically proportional ton
(d−1)/(d+1), which generalizes Rényi and Sulanke’s asymptotic raten
(1/3) ford=2 and agrees with Raynaud’s asymptotic raten
(d−1)/(d+1) for the expected number of facets, as it should be, by Bárány’s result that the expected number ofs-dimensional faces has order of magnitude independent ofs. Our formulas agree with the ones Efron obtained ford=2 and 3 under more general distributions. An application is given to the estimation of the probability content of an unknown
convex subset ofR
d
. 相似文献
5.
6.
David Gilat Isaac Meilijson Laura Sacerdote 《Stochastic Processes and their Applications》2018,128(6):1849-1856
For a martingale starting at with final variance , and an interval , let be the normalized length of the interval and let be the normalized distance from the initial point to the lower endpoint of the interval. The expected number of upcrossings of by is at most if and at most otherwise. Both bounds are sharp, attained by Standard Brownian Motion stopped at appropriate stopping times. Both bounds also attain the Doob upper bound on the expected number of upcrossings of for submartingales with the corresponding final distribution. Each of these two bounds is at most , with equality in the first bound for . The upper bound on the length covered by during upcrossings of an interval restricts the possible variability of a martingale in terms of its final variance. This is in the same spirit as the Dubins & Schwarz sharp upper bound on the expected maximum of above , the Dubins & Schwarz sharp upper bound on the expected maximal distance of from , and the Dubins, Gilat & Meilijson sharp upper bound on the expected diameter of . 相似文献
7.
Isaac Meilijson 《Israel Journal of Mathematics》1974,19(3):266-270
Skew-products of the powers of an ergodic measure preserving transformation with a Bernoulli base are shown to bek-automorphisms. 相似文献
8.
Gilat David Meilijson Isaac Sacerdote Laura 《Journal of Theoretical Probability》2022,35(3):1952-1955
Journal of Theoretical Probability - For an $${\text {L}}_2$$ -bounded martingale starting at 0 and having final variance $$\sigma ^2$$ , the expected local time at $$a \in \text {R}$$ is at most... 相似文献
9.
Isaac Meilijson 《Israel Journal of Mathematics》1973,15(2):193-203
The behavior of (1/N)
asN→∞ is considered, wheref is a bounded measurable function on (−∞, ∞) and (S
n)
n
=1/∞
are the partial sums of a sequence of independent and identically distributed rondom variables. 相似文献
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