New Perspectives on Random Fields with Applications

随机场及其应用的新视角

• 批准号: 0404729
• 负责人: Davar Khoshnevisan
• 金额: $ 27.37万
• 依托单位: University of Utah
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-08-15 至 2008-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0404729&HistoricalAwards=false
• 关键词: New; Perspectives; Random; Fields; Applications

0404729Khoshnevisan One of the primary concerns of this project is to develop a systematic geometrical analysis of random fields. Special emphasis is placed on investigating some of the random fields that arise in pure and applied mathematics, statistics, mathematical oceanography, mathematical hydrology, and mathematical physics. This research is to gather and develop probabilistic, analytic, algebraic, and geometric tools that lead to a deeper understanding of the geometry of random fields. It is expected that the contributions of this proposal may help solve a number of long-standing open problems in the theories of Levy processes and Brownian sheet, and promote applications of such random fields in the aforementioned areas.

[404729] khoshnevisan该项目的主要关注点之一是对随机场进行系统的几何分析。特别强调的是研究在纯数学和应用数学、统计学、数学海洋学、数学水文学和数学物理中出现的一些随机场。这项研究是为了收集和发展概率、解析、代数和几何工具，从而更深入地了解随机场的几何形状。期望本文的贡献有助于解决Levy过程和布朗表理论中一些长期存在的开放性问题，并促进这些随机场在上述领域的应用。