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.

9803747Khoshnevisanthis Grant为犹他大学为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在随机领域研究中自然出现的特殊集合。 特殊重点将放在高斯随机场（例如布朗尼纸和小部分运动）上。 更具体地说，这些研究者将（1）研究随机字段，能力和较高级数部分微分方程之间的精确定量连接； （2）开发和推进规范技术，用于对大类高斯随机场的多骨架和几何分析； （3）继续他们在维纳空间中的高斯过程和能力理论之间建立联系方面的持续工作； （4）继续研究一类随机不稳定的表面和结构上的规范热流。这项研究将研究高斯随机场的性质，例如布朗尼薄板和分数布朗尼运动。 这些是随机领域，在经济学，海洋学，水文学和物理学的数学和数学方面的几个学科中起着重要作用。 拟议研究的目的是开发分析工具，这将使对随机领域的几何问题有更好的了解，并有助于促进其进一步的适用性。