Random Fields and Potential Theory

随机场和势论

• 批准号: 9803747
• 负责人: Davar Khoshnevisan
• 金额: $ 16.05万
• 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: 1998
• 资助国家: 美国
• 起止时间: 1998-08-01 至 2002-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9803747&HistoricalAwards=false
• 关键词: Random; Fields; Potential; Theory

9803747KhoshnevisanThis grant provides funds for Davar Khoshnevisan and Yimin Xiao at the University of Utah to develop a systematic approach to the study of many of the exceptional sets which naturally arise in the study of random fields. Special emphasis will be placed on Gaussian random fields such as the Brownian sheet and fractional Brownian motion. More specifically, these investigators will (1) study precise quantitative connections between random fields, capacities and higher--order partial differential equations; (2) develop and advance canonical techniques for the multi-fractal and geometric analysis of a large class of Gaussian random fields; (3) continue their on-going work on developing connections between the theory of Gaussian processes and capacity in Wiener space; and (4) continue their investigation of canonical heat flow on a class of random erratic surfaces and structures.This research will study the properties of Gaussian random fields, such as the Brownian sheet and fractional Brownian motion. These are random fields which play a prominent role in several disciplines in mathematics and mathematical aspects of economics, oceanography, hydrology and physics. The goal of the proposed research is to develop analytical tools which will lead to a better understanding of geometric problems for random fields and help promote their further applicability.

9803747 Khoshnevisan这笔赠款为犹他州大学的Davar Khoshnevisan和Yimin Xiao提供资金，以开发一种系统的方法来研究许多自然出现在随机场研究中的例外集。 特别强调将放在高斯随机场，如布朗单和分数布朗运动。 更具体地说，这些研究人员将（1）研究随机场、容量和高阶偏微分方程之间的精确定量联系;（2）发展和推进一大类高斯随机场的多重分形和几何分析的规范技术;（3）继续他们正在进行的关于发展Wiener空间中高斯过程理论和容量之间联系的工作;（4）继续研究一类随机无规表面和结构上的正则热流，研究高斯随机场的性质，如布朗单和分数布朗运动。 这些是随机领域发挥了突出的作用，在几个学科的数学和数学方面的经济学，海洋学，水文学和物理学。 拟议的研究的目标是开发分析工具，这将导致更好地理解随机场的几何问题，并有助于促进其进一步的适用性。