Mathematical Sciences: Topics in Heavy Tailed Modelling

这是一个为期三年的研究计划，围绕重尾建模的主题组织。重尾模型假设规则变化存在于系统的基本分量分布的右尾（通常意味着无穷大的方差）或左尾，因此偏离高斯方法。广泛的主题包括参数估计和预测重尾模型（希尔估计，线性规划估计），模型选择和确认和长期依赖。要研究的具体类别的模型是极值模型，无限可分的过程和时间序列的积极创新。应用领域包括建模金融和商品市场和远程交通系统。 这是一个为期三年的研究计划，围绕两个主题组织。第一种方法涉及对随机现象进行建模，这些现象的行为由非常大的值控制。例如，在通信中，网络性能可能会受到异常长时间调用（例如通过调制解调器登录计算机）的显著影响。对这些现象进行准确建模可以改进系统。第二个主题涉及系统中的依赖关系持续很长时间的随机现象。 准确的建模在提高系统性能方面同样重要。这项研究的其他应用包括金融和商品市场建模以及水流和高度建模。

This is a three year program of research organized around the theme of heavy tailed modeling. Heavy tailed modeling assumes regular variation is present in either the right tail (frequently implying infinite variances) or the left tail of basic component distributions of the system and thus departs from Gaussian methods. Broad themes include parameter estimation and prediction in heavy tailed models (Hill estimator, linear programming estimator), model selection and confirmation and long range dependence. Specific classes of models to be studied are extreme value models, infinitely divisible processes and time series with positive innovations. Application areas include modeling financial and commodities markets and teletraffic systems. This is a three year program of research organized around two topics. The first involves modeling random phenomena whose behavior is controlled by exceedingly large values. For example, in communications, network performance can be dramatically affected by anomalous long calls such as computer logins by modem. Accurate modeling of these phenomena can lead to improvements in the system. The second topic deals with random phenomena in which dependencies in a system last a long time. Once again accurate modeling is important in improving system performance. Other applications of this research include modeling financial and commodities markets and modeling of water flows and heights.