Mathematical Sciences: Some Problems on Laws of the IteratedLogarithm and Strong Approximations

数学科学：关于迭代对数定律和强近似的一些问题

• 批准号: 9207248
• 负责人: Uwe Einmahl
• 金额: $ 4万
• 依托单位: Indiana 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: 1993-06-01 至 1995-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9207248&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Some; Problems; Laws

One of the basic results of probability is the so-called law of the iterated logarithm (LIL), which provides a precise description of the asymptotic behavior of sums of independent random variables. For many applications one needs a more general framework than in the classical case which deals with real-valued random variables. The main purpose of this research is to study LIL results and some related problems such as strong approximation and certain weak convergence results in general Banach spaces. This research will extend results in the theory of probability. In many applications a more general framework is needed, and this research will help provide it.

概率论的一个基本结果是所谓的迭代对数定律（LIL），它精确地描述了独立随机变量和的渐近行为。对于许多应用，我们需要一个比处理实值随机变量的经典情况更通用的框架。本研究的主要目的是研究一般Banach空间中的LIL结果以及一些相关的问题，如强逼近和某些弱收敛结果。这项研究将扩展概率论的成果。在许多应用中需要一个更通用的框架，而本研究将有助于提供它。