Mathematical Sciences: Tail Probability Approximations for Sums of Dependent Variables

数学科学：因变量之和的尾部概率近似

• 批准号: 9310682
• 负责人: Victor de la Pena
• 金额: $ 6万
• 依托单位: Columbia University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-07-15 至 1996-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9310682&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Tail; Probability; Approximations

This research is to study the problem of obtaining an accurate description of the probabilistic behavior of sums of dependent random variables. Essential tools for the proposed work will be recent results in the area of decoupling inequalities. A decoupling inequality transforms problems on sums of dependent random variables to problems on sums of conditionally independent random variables. In the proposed work, particular attention will be focused on developing tail probability approximations for randomly stopped sums, quadratic forms of independent random variables, and the general problem of sums of arbitrarily dependent random variables. This research is to study some important problems in probability theory. In particular, the investigator will look at the behavior of sums of dependent observations. These sums will be studied by comparing them to appropriate sums of independent observations.

本研究旨在研究如何准确地刻画相依随机变量和的概率行为。拟议工作的基本工具将是脱钩不平等领域的最新成果。解耦不等式将相依随机变量之和问题转化为条件独立随机变量之和问题。在所提出的工作中，将特别关注发展随机停止和的尾概率近似，独立随机变量的二次型，以及任意相依随机变量和的一般问题。本研究旨在研究概率论中的一些重要问题。特别是，调查者将研究相依观察值的总和的行为。这些总和将通过将它们与适当的独立观测总和进行比较来研究。