Theory and Applications of Heavy Tails and Long Range Dependence

PI提出了一种通过相变来考虑长程依赖的新方法，它扩展了典型的关于不可靠存在的乘积矩的思维。这样的方法可能会导致新的研究方向，例如概率理论和遍历理论之间的新联系。此外，还将研究与重尾相关的各种困难问题，包括高维问题、可视化问题、最小距离方法的影响以及渐近充分性。应用领域包括金融工程、数据网络、水文、气象和环境研究、风险分析。Sidney Resnick和Gennady Samorodnitsky的一个为期三年的研究计划将处理关于重尾和/或长程相关性现象的理论和实践问题。长期依赖是一种模型的性质，在该模型中，依赖持续时间非常长。模型展示了重尾，容易受到特别大的冲击。这两个概念实际上都很重要(在互联网建模、金融、可靠性方面)，在理论上也具有挑战性。

The PIs propose a new approach to thinking about long range dependence by means of phase transitions, which extends typical thinking in terms of product moments which exist unreliably. Such an approach will likely lead to new directions of research, for example to new connections between probability theory and ergodic theory. Furthermore, various difficult issues concerning heavy tails will be investigated, including high dimension problems, visualization problems, impact of minimum distance methodology and asymptotic sufficiency. Application areas include financial engineering, data networks, hydrology, meteorology and environmental studies, risk analysis. A three year program of research by Sidney Resnick and Gennady Samorodnitsky will deal with theoretical and practical problems about phenomena with heavy tails and/or long range dependence. Long range dependence is a property of a model in which dependence persists over exceptionally long time periods. Heavy tails are exhibited by model subject to particularly large shocks. Both notions are practically important (in internet modeling, finance, reliability ) and theoretically challenging.