Random Fields and Stochastic Partial Differential Equations

随机场和随机偏微分方程

• 批准号: 0706728
• 负责人: Davar Khoshnevisan
• 金额: --
• 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: 2007
• 资助国家: 美国
• 起止时间: 2007-07-01 至 2011-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0706728&HistoricalAwards=false
• 关键词: Random; Fields; Stochastic; Partial; Differential

One of the primary concerns of this proposal is to develop, systematically, geometric methods for analysisof random fields and stochastic differential equations. Special emphasis isplaced on Gaussian, stable, and Levy random fields such as theBrownian sheet, additive Levy processes, and solutions ofstochastic partial differential equations driven by Gaussian orLevy noises. These are random fields that arise naturally inmany areas of mathematics, applied mathematics, mathematicaloceanography, turbulence, stochastic hydrology, geostatistics, spatial statistics, and mathematical physics. The proposed research intends to gather and develop probabilistic, analytic, algebraic, and geometric tools that lead to a deeper understanding of the geometry of random fields and stochastic partial differential equations. The Proposers believe that these tools will be novel enough to solve a number of open problems on random fields. The Proposers also believe thatthe program developed herein will help promote the future applicability of these and related mathematical methods in theaforementioned areas.

该提案的主要关注点之一是系统地开发用于分析随机场和随机微分方程的几何方法。特别强调高斯、稳定和 Levy 随机场，例如布朗片、加性 Levy 过程以及由高斯或 Levy 噪声驱动的随机偏微分方程的解。这些是在数学、应用数学、数学海洋学、湍流、随机水文学、地质统计学、空间统计学和数学物理学的许多领域中自然出现的随机场。拟议的研究旨在收集和开发概率、分析、代数和几何工具，以加深对随机场和随机偏微分方程几何的理解。提议者相信这些工具足够新颖，可以解决随机领域的许多开放问题。提案者还相信，本文开发的程序将有助于促进这些以及相关数学方法在上述领域的未来适用性。