Long Range Dependence, Heavy Tails and Communication Networks

该项目的重点是长期依赖和重尾之间的联系。主要应用领域是数据网络、金融、精算研究和工业工程。该项目包括考虑与检测长程相关性，自相似性和多重分形相关的统计问题，以及基本概念定义不充分的基本问题。例如，长程相关性通常是根据相关性来定义的，但这些相关性可能由于存在重尾而不确定，或者对于非高斯过程来说，这些相关性是没有信息的。 我们的社会是一个快速移动和变化的社会，越来越多的信息从国家的一端转移到另一端。技术和科学的巨大进步往往是日常现象。股票市场波动很大。互联网和其他通信网络容易出现过载和延迟，由于它们在我们的经济和公共生活中发挥着至关重要的作用，人们需要关注它们的性能。需要适当的模型来理解这些剧烈振荡的过程。该项目的重点是适合于理解和控制这些现象的模型-具有重尾和/或长程依赖性的模型。

This project is centered on connections between long range dependence and heavy tails. The primary application areas are data networks, finance, actuarial research and industrial engineering. The project includes a consideration of statistical issues related to detection of long range dependence, self-similarity and multifractality as well as fundamental issues of basic concepts being inadequately defined. For instance, long range dependence is often defined in terms of correlations but these may be either undefined due to the presence of heavy tails or for non-Gaussian processes rather uninformative. Our society is a fast moving and changing one, with ever increasing amounts of information being moved from one end of the country to the other. Dramatic technological and scientific advances are, often, day-to-day phenomena. The stock market is very volatile. The Internet and other communication networks are susceptible to overloads and delays and because of their crucial role in our economic and public life, one needs to be concerned with their performance. Appropriate models are required to make sense of these wildly oscillating processes. This project is centered on models appropriate to understanding and controlling these phenomena-- models with heavy tails and/or long range dependence.