Contemporary Problems in Probability and Statistics:Gaussian Approximations and Small Deviations for Stochastic Processes

当代概率与统计问题：随机过程的高斯近似和小偏差

• 批准号: 323605340
• 负责人: Professor Dr. Friedrich Götze
• 金额: --
• 依托单位: Laboratory of Algebra and Number Theory Petersburg
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2017
• 资助国家: 德国
• 起止时间: 2016-12-31 至 2021-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/323605340?language=en
• 关键词: Contemporary; Problems; Probability; Statistics; Gaussian

The aim of this project is to investigate selected approximation problems in the field of probability theory and statistics as a joint effort of research groups from Germany and St. Petersburg. A common feature of all subprojects are Gaussian finite and infinite dimensional approximations and their generalizations. They range from classical problems for the approximation of sums of independent identically distributed random variables and vectors to maxima of sums of stationary random variables and optimal approximation of stochastic processes by classes of smooth processes weighted by generalized Sobolev norms. This has applications in various fields, e.g. statistics, image processing andapproximation of complex spectra of random matrices A common theme of central interest is the control of small ball probabilities where the participants of this application could benefit from the considerable expertise of the research groups in Germany and Russia.

该项目的目的是研究概率理论和统计领域中选定的近似问题，作为来自德国和圣彼得堡研究小组的共同努力。所有副投影的一个共同特征是高斯有限和无限尺寸近似及其概括。它们的范围从经典问题到独立分布的随机变量和向量的近似值到固定随机变量的最大值，以及通过广义Sobolev规范加权的平滑过程的类别对随机过程的最佳近似。这在各个领域都有应用，例如 随机矩阵的复杂光谱的统计数据，图像处理和应用程序的一个共同主题是控制小球概率的控制，在该概率中，本申请的参与者可以从德国和俄罗斯的研究小组的大量专业知识中受益。