Stochastic Analysis and its Applications

随机分析及其应用

• 批准号: 0303310
• 负责人: Krzysztof Burdzy
• 金额: $ 24.8万
• 依托单位: University of Washington
• 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 2007-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0303310&HistoricalAwards=false
• 关键词: Stochastic; Analysis; its; Applications

The PIs investigate several problems in stochastic analysis of both a pure and applied nature. Inverse problems and the third boundary problem are mathematical models arising naturally in applied sciences from geophysics to medicine and physics. The PIs study the foundational questions related to these models, such as existence and uniqueness of the solutions to the corresponding equations, and also address specific problems in each of these fields. The PI's investigate several aspects of reflected Brownian motion, including the coalescence of synchronous couplings, reflection with inert drift, existence of shy couplings, construction of reflected processes via myopic conditioning, and the pathwise uniqueness for the Skorohod equation. Other models and processes are the subject of separate but related studies; they include the skew Brownian motion stochastic flow, censored stable processes, and jump-type processes. The PI's attack some well known "open problems" on Neumann eigenfunctions and reflected Brownian motion. The project is devoted to modeling, at the mathematical level, of natural, technical, economic and social phenomena involving randomness. The field of stochastic analysis arose as a need to understand phenomena as diverse as the stock market, non-destructive analysis of materials, medical imaging, and heat dissipation. The mathematical side of the project provides a foundation for the applications such as computer programs that help in real life situations. The applied sciences routinely use mathematical formulas of stochastic analysis. The project aims at providing usable information about stochastic processes.

PI研究了纯粹和应用性质的随机分析中的几个问题。反问题和第三边值问题是从物理学到医学和物理学的应用科学中自然产生的数学模型。PI研究与这些模型相关的基础问题，例如相应方程解的存在性和唯一性，并解决每个领域的具体问题。PI的调查反射布朗运动的几个方面，包括合并的同步耦合，反射与惰性漂移，存在害羞的耦合，建设反射过程通过近视条件反射，和路径的唯一性为Skorohod方程。其他模型和过程是独立但相关研究的主题;它们包括斜布朗运动随机流，删失稳定过程和跳跃型过程。PI对Neumann本征函数和反射布朗运动的一些著名的“公开问题”的攻击。 该项目致力于在数学层面上对涉及随机性的自然、技术、经济和社会现象进行建模。随机分析领域的出现是因为需要了解股票市场，材料的非破坏性分析，医学成像和散热等各种现象。数学方面的项目提供了一个基础的应用程序，如计算机程序，帮助在真实的生活情况。应用科学通常使用随机分析的数学公式。该项目旨在提供有关随机过程的有用信息。