Theory and Applications of Heavy Tails and Long Range Dependence

重尾和长程相关的理论与应用

• 批准号: 0303493
• 负责人: Gennady Samorodnitsky
• 金额: $ 21.3万
• 依托单位: Cornell University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-07-15 至 2006-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0303493&HistoricalAwards=false
• 关键词: Theory; Applications; Heavy; Tails; Long

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.

PI提出了一种新的方法来思考长程依赖的相变，这扩展了典型的思维方式的产品的时刻存在不可靠。这种方法可能会导致新的研究方向，例如概率论和遍历理论之间的新联系。此外，各种困难的问题，包括高维问题，可视化问题，最小距离方法的影响和渐近充分性的重尾将进行研究。应用领域包括金融工程、数据网络、水文学、气象学和环境研究、风险分析。西德尼·雷斯尼克和根纳季·萨莫罗德尼茨基的一项为期三年的研究计划将处理有关重尾和/或长程依赖现象的理论和实际问题。长程相关性是模型的一个特性，其中相关性持续非常长的时间段。受到特别大的冲击的模型显示出重尾。这两个概念在实践中都很重要（在互联网建模、金融、可靠性方面），在理论上也具有挑战性。