Mathematical Sciences: Laws of the Iterated Logarithm and Strong Approximations

数学科学：迭代对数定律和强近似

• 批准号: 9005804
• 负责人: Uwe Einmahl
• 金额: $ 2.75万
• 依托单位: Indiana University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-06-15 至 1992-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9005804&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Laws; Iterated; Logarithm

The principal investigator is working on problems in probability theory concerning the law of the iterated logarithms (LIL) and strong approximations. In particular, the investigator will work on convergence rates in the LIL in Hilbert spaces, infinite dimensional versions of the Darling-Erdos theorem and Chung type LIL's, and strong approximations for sums of independent Banach space value random variables. Properties of sums of independent random variables have been of interest to probabilists and statisticians for a long time. The law of the iterated logarithm gives a very precise bound on how fast a sum of random variables grows.

首席研究员正在研究概率论中关于重对数律(LIL)和强逼近的问题。特别地，研究者将研究Hilbert空间中LIL的收敛速度，Darling-Erdos定理和Chung型LIL的无穷维版本，以及独立Banach空间值随机变量和的强逼近。独立随机变量和的性质长期以来一直是概率学家和统计学家感兴趣的问题。重对数律给出了随机变量和增长速度的一个非常精确的界限。