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11.
Dan Voiculescu 《Reports on Mathematical Physics》2005,55(1):127-133
This short note summarizes the circumstances of the birth of free probability theory andsome of the recent achievements. 相似文献
12.
Arnon Arazi Eshel Ben-Jacob Uri Yechiali 《Mathematical Methods of Operations Research》2005,62(3):453-466
We consider a Jackson-type network comprised of two queues having state-dependent service rates, in which the queue lengths
evolve periodically, exhibiting noisy cycles. To reduce this noise a certain heuristic, utilizing regions in the phase space
in which the system behaves almost deterministically, is applied. Using this heuristic, we show that in order to decrease
the probability of a customers overflow in one of the queues in the network, the server in that same queue – contrary to intuition
– should be shut down for a short period of time. Further noise reduction is obtained if the server in the second queue is
briefly shut down as well, when certain conditions hold. 相似文献
13.
We establish a relation between stable distributions in probability theory and the fractional integral. Moreover, it turns out that the parameter of the stable distribution coincides with the exponent of the fractional integral. It follows from an analysis of the obtained results that equations with the fractional time derivative describe the evolution of some physical system whose time degree of freedom becomes stochastic, i.e., presents a sum of random time intervals subject to a stable probability distribution. We discuss relations between the fractal Cantor set (Cantor strips) and the fractional integral. We show that the possibility to use this relation as an approximation of the fractional integral is rather limited. 相似文献
14.
稀疏过程在破产问题中的应用 总被引:5,自引:0,他引:5
本讨论一类人寿保险的风险过程,其中保单到达服从齐次Poisson过程。而描述退保及索赔发生的计数过程分别为这一过程的q-稀疏与p-稀疏.对此模型给出其破产概率的具体上界,并与其它一类风险模型进行比较. 相似文献
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16.
Hans TRIEBEL 《应用数学学报(英文版)》2004,(4)
The paper deals with multifractal quantities for some types of Radon measures,especiallyself-similar probability measures,and their relations to Besov spaces. 相似文献
17.
The form of the probability density derived from the evolution in time of a previously truncated frequency distribution of animal Liveweights is of interest in animal husbandry. Truncated frequency distributions arise when the heavier animals are sold for slaughter and the lighter animals retained. The demands of modern quality assurance schemes require that, given information on animal growth, the farmer is able to estimate the number of animals that would meet the specifications at some time in the future after truncation. Assuming that animal growth can be described by a linear stochastic differential equation, we derive an explicit expression for the probability density of animal Liveweights at any time after the truncation of an initial Gaussian density. It is shown that this probability density converges rapidly to a Gaussian density, so that after about 20 days of typical growth rates for lambs, the resulting density is practically indistinguishable from Gaussian. 相似文献
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19.
Recently, Fishbum and Lavalle (1995) and Lefèvre and Utev (1996) have considered some stochastic order relations specific for arithmetic random variables. The present work is concerned with these orderings, together with two other classes of stochastic order relations closely related. First, attention is paid to characterizations and various properties of all these orderings. Then, sufficient conditions of crossing-type for the two new classes of orderings are derived and extrema among discrete random variables are deduced. This is applied in actuarial sciences to obtain new bounds for the classical single life premiums as well as for the probability of ruin in the compound binomial risk model. 相似文献
20.
Hidetoshi Shimodaira 《Annals of the Institute of Statistical Mathematics》1997,49(3):395-410
The asymptotic error probability of Linhart's model selection test isevaluated, and compared with the nominal significance level. We examine thecase where the expected discrepancies of the candidate models from the truemodel are asymptotically equal. The local alternatives method is employed inthe limiting operation of the asymptotic evaluation. Although the errorprobability under the null hypothesis is actually shown to be equal to orless than the level for most situations, intolerable violations of the errorcontrol are observed for nested models: It is often erroneously concludedthat the smaller model is significantly better than the larger model. Toprevent this violation, a modification of Linhart's test statistic isproposed. The effectiveness of the proposed test is confirmed throughtheoretical analysis and numerical simulations. 相似文献