Mathematical Sciences: Brownian Motion, Martingales and Applications

数学科学：布朗运动、鞅及其应用

• 批准号: 8901164
• 负责人: Rodrigo Banuelos
• 金额: $ 4.17万
• 依托单位: Purdue Research Foundation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-06-01 至 1992-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8901164&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Brownian; Motion; Martingales

This research will focus on problems in two areas of martingales and their applications. First, the project will be study of laws of the iterated logarithm for harmonic functions and related questions. Second, the research will involve analysis of the inequalities for martingale transforms and projections of martingale transforms with applications to Riesz transforms and determination of the best constant in an inequality for the Haar functions. This research is in the general area of statistics and probability and consists of applying probabilistic techniques to problems in analysis. The work involves finding optimal or near optimal constants in a number of classical inequalities. Ten years ago such problems would have appeared unsolvable. Today the situation has changed completely and a number of important problems in several fields have been shown to reduce to the determination of certain constants in analytic inequalities.

这项研究将集中在两个领域的问题， 鞅及其应用 首先，该项目将 调和函数重对数律的研究 及相关问题。 第二，研究将涉及 鞅变换不等式的分析和 鞅变换的投影及其对Riesz的应用 变换和最佳常数的确定 Haar函数的不等式 这项研究属于一般统计领域， 概率，包括应用概率技术， 问题分析。 这项工作涉及寻找最佳或接近 一些经典不等式中的最优常数。 十 如果放在几年前，这些问题似乎是无法解决的。 今天 情况已经完全改变， 已经表明，几个领域中的问题减少到 解析不等式中某些常数的确定。