Mathematical Sciences: Large Deviations and the Law of the Iterated Logarithm in Banach Spaces

数学科学：巴纳赫空间中的大偏差和迭代对数定律

• 批准号: 8709388
• 负责人: Alejandro de Acosta
• 金额: $ 4.23万
• 依托单位: Case Western Reserve University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-07-01 至 1989-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8709388&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Large; Deviations; Law

The investigator plans to study two problems. The first problem of large deviations has deep theoretical consequences as well as applications in statistical physics and mathematical statistics. The investigator hopes eventually to prove a general result on lower bounds for large deviations in case of vector- valued functionals of Markov chains. He has already established several links necessary to prove this result. The second problem hopes to settle the major open question in the field of the law of iterated logarithms in Banach spaces viz., the identification of the limits and the underlying problem of obtaining sharp exponential bounds for sums of independent random vectors.

研究者计划研究两个问题。第一个大偏差问题在统计物理和数理统计中有着深刻的理论影响和应用。研究者希望最终证明一个关于马尔可夫链的向量值泛函的大偏差下界的一般结果。他已经建立了几个必要的环节来证明这一结果。第二个问题希望解决巴拿赫空间中迭代对数律领域的主要开放性问题，即极限的识别和获得独立随机向量和的尖锐指数界的潜在问题。